Europe began to throw off some of its self-imposed constraints on helping Ukraine militarily during the past week, as the United States remained cautious and Russia warned against actions that could cause “a World War” – an oft-repeated threat to use nuclear weapons.

On the ground, Ukraine arrested the Russian advance in its northern Kharkiv region, taking back some territory northeast of Lyptsi, and held the defence of Chasiv Yar, a strategically important town on the eastern front.

Its Military Media Center said on Sunday it had killed or wounded 8,650 Russian soldiers in a week, the equivalent of 17 battalions, and destroyed 81 tanks and 153 armoured vehicles. Ukrainian President Volodymyr Zelenskyy said Russian losses in Kharkiv were eight times Ukraine’s.

But he warned that new Russian offensive forces were building up in Belgorod, northwest of Kharkiv.

Al Jazeera was unable to independently verify the toll and figures announced by Ukraine.

French President Emmanuel Macron said on Sunday he would allow Ukraine to use French weapons to strike inside Russia – a demand Ukraine has raised with new urgency since the Kharkiv incursion on May 10.

“We think that we should allow them to neutralise the military sites from which the missiles are fired and, basically, the military sites from which Ukraine is attacked,” Macron said during a news conference with German Chancellor Olaf Scholz during a three-day trip to Germany.

“Ukrainian soil is being attacked from bases in Russia. So how do we explain to the Ukrainians that we’re going to have to protect these towns … if we tell them you are not allowed to hit the point from which the missiles are fired?”

Macron clarified that civilian facilities could not be targeted.

His statement came a day after Russia fired missiles into a shopping centre in Kharkiv, burning it to the ground, killing 16 people and hospitalising 45. Many are still missing.

“This attack on Kharkiv is another manifestation of Russian madness. There is simply no other way to call it. Only madmen like Putin are capable of killing and terrorising people in such a vile way,” Zelenskyy declared.

Ukraine’s air defences often aren’t sufficient to intercept hailstorms of missiles and drones fired from Russia and Crimea, and Ukraine has said it needs to strike Russia’s missile launch sites and airfields.

From those airfields, Russia flies out aircraft that drop roughly 3,000 glide bombs a month – massive munitions usually weighing 250kg or 500kg (550lb or 1100lb) – which military analysts say have done much to give it the initiative on the front lines.

Currently, Ukraine can only down the bombers that deliver these glide bombs, and it did so twice this week, when it shot down Sukhoi-25s over Kharkiv on May 22 and Donetsk the following day. It has also partially blinded Russian pilots by grounding their A-50 radar planes that facilitate reconnaissance and targeting.

But that is not enough, says Ukraine, because Russian missiles, glide bombs and drones keep coming, and now there are new ground invasions. It also needs to hit airfields, missile launch sites and offensive battalions marshalling on Russian soil a few kilometres from the Ukrainian border.

Standing in a bombed-out printing press in Kharkiv on Sunday, Zelenskyy said a new ground invasion was imminent: “Russia is preparing for offensive actions also 90km [56 miles] northwest from here – they gather another group of troops near our border,” he told reporters.

Currently, Ukraine is only able to strike Russia with its Soviet-era S-200/S-300 air defence missiles or domestically produced drones, which carry small charges and are easily shot down by Russian air defences.

Ukraine’s NATO allies have begun to recognise this, and on Monday the NATO Parliamentary Assembly voted to expand the use of weapons and speed up their delivery.

The adopted Declaration 489 called on allies “to support Ukraine in its international right to defend itself by lifting some restrictions on the use of weapons provided by NATO Allies to strike legitimate targets in Russia”.

Most remarkably, NATO chief Jens Stoltenberg went against the policy of the alliance’s largest member, the US, to urge allies to do so.

“The time has come for allies to consider whether they should lift some of the restrictions they have put on the use of weapons they have donated to Ukraine,” Stoltenberg told The Economist.

“Especially now when a lot of the fighting is going on in Kharkiv, close to the border [with Russia], to deny Ukraine the possibility of using these weapons against legitimate military targets on Russian territory makes it very hard for them to defend themselves.”

Macron is not the first NATO leader to lift the restrictions.

Britain’s foreign secretary, David Cameron, did so during a visit to Kyiv on May 3.

France and the United Kingdom have since May 2023, provided Ukraine with the 250km-range (155-mile) Scalp/Storm Shadow missile, for a year its longest-range weapon, joined last month by the 300km-range (186-mile) ATACMS being provided by the US.

Despite the NATO declaration, the US Pentagon’s spokeswoman, Sabrina Singh, said on Wednesday, “Our position hasn’t changed in terms of how we believe the Ukrainians can be successful on the battlefield. But I leave it to other countries to speak to their own weapons that they provide.”

But its position appeared to be the subject of debate.

The New York Times reported that Secretary of State Antony Blinken was in disagreement with other cabinet members over the prohibition against using US weapons in Russia.

During a visit to Kyiv on May 15, Blinken had said, “We have not encouraged or enabled strikes outside of Ukraine, but ultimately Ukraine has to make decisions for itself about how it’s going to conduct this war,” a statement that seemed to hint at a shift in policy.

Sergey Lavrov, Russia’s foreign minister, told a news conference in Belarus on Friday that the White House was in no dilemma at all: “Washington is trying … to pretend the decision has not yet been made. It is a trick. We are certain that American and other Western-supplied weapons are being used to strike targets on Russian territory.”

Germany, the other major holdout, shifted towards Macron’s position on Monday, when Chancellor Scholz told reporters Ukraine could strike military sites within Russia.

“Ukraine has every possibility to do this, under international law,” Scholz said. “It must be said clearly, if Ukraine is attacked, it can defend itself.”

Scholz did not also shift on providing 500km-range (316-mile) Taurus missiles, which Germany produces, and Ukraine has asked for.

Russian President Vladimir Putin wasted no time warning that there would be “serious consequences” should Ukraine use European weapons inside Russia, and the traditionally frank Dmitry Medvedev, deputy head of Russia’s Security Council, wrote on X that “Americans hitting our targets means starting a world war”.

France, meanwhile, was already holding talks on lifting another NATO taboo and sending its troops to train Ukrainian units inside Ukraine – something Stoltenberg did not endorse.

Ukrainian Commander-in-Chief Oleksandr Syrskii announced on Telegram that French instructors would “visit” training facilities on Ukrainian soil soon.

“I welcome France’s initiative to send instructors to Ukraine to train Ukrainian military personnel,” he wrote on Monday. “I have already signed the documents that will allow the first French instructors to visit our training centres soon.”

Poland, another leading Ukraine ally, has said it was considering felling another taboo – shooting down incoming Russian missiles from its own airspace. Ukraine asked its allies to do this after an international task force in the Red Sea helped shoot down 307 Iranian missiles and drones bound for Israel on April 13.

Ukraine also signed three new multiyear bilateral military agreements during the week, with Spain, Belgium and Portugal. Spain and Belgium each promised 1 billion euros ($1.1bn) in aid this year, and Belgium said it would send 30 F-16 fighter jets to Ukraine by 2028. Ukraine has said it needs 120-130 F-16s to defend its airspace.

Not everyone in the alliance was on board with accelerating and expanding military aid to Ukraine.

Hungary’s Viktor Orban told Kossuth Radio that he was not satisfied that NATO would not become a party to the conflict and that Brussels had “task forces working on ways for NATO to take part in this war”.

“Hungary is opposed to this. The government is working intensively to figure out how to avoid participating in the war while remaining a NATO member,” Russian state news agency TASS quoted Orban as saying. “There aren’t many situations in NATO’s history where member states openly took a distinct stance like Hungary is now doing.”

Hungary maintains strong economic and energy ties with Russia and has forbidden military aid to transit its territory en route to Ukraine.