Six people have drowned in Austria, Poland and Romania and four others are missing in the Czech Republic as Storm Boris continues to lash central and eastern Europe, bringing torrential rain and floods that have forced the evacuation of thousands of people from their homes.

Swathes of Austria, the Czech Republic, Hungary, Romania and Slovakia have been battered by high winds and unusually fierce rains since Thursday.

Austria’s vice-chancellor, Werner Kogler, said on Sunday that a firefighter had died tackling flooding in Lower Austria, as authorities declared the province, which surrounds the capital, Vienna, a disaster area.

Some areas of the Tirol were blanketed by up to a metre (3ft) of snow – an exceptional situation for mid-September, which saw temperatures of up to 30C (86F) last week.

Rail services were suspended in the country’s east early on Sunday and several metro lines were shut down in Vienna, where the Wien River was threatening to overflow its banks, according to the APA news agency.

Emergency services made nearly 5,000 interventions overnight in Lower Austria where flooding had trapped many residents in their homes. Firefighters have intervened about 150 times in Vienna since Friday to clear roads blocked by storm debris and pump water from cellars, local media reported.

Poland’s prime minister, Donald Tusk, said one person in the Kłodzko region had drowned. Tusk was travelling through the south-west of the country, which has been hit hardest by the floods. About 1,600 people have been evacuated in Kłodzko, and Polish authorities have called in the army to support firefighters on the scene.

“The situation is very dramatic,” Tusk said on Sunday after a meeting in Kłodzko, which was partly under water as the local river rose to 6.7 metres on Sunday morning – well above the alarm level of 2.4 metres – before receding slightly. That surpassed a record set during heavy flooding in 1997, which partly damaged the town and claimed 56 lives.

On Saturday, Polish authorities shut the Gołkowice border crossing with the Czech Republic after a river flooded its banks, as well as closing several roads and halting trains on the line linking the towns of Prudnik and Nysa.

In the nearby village of Głuchołazy, Zofia Owsiaka watched with fear as the fast-flowing waters of the swollen Biała river surged past. “Water is the most powerful force of nature. Everyone is scared,” said Owsiaka, 65.

In Budapest, officials raised forecasts for the Danube to rise in the second half of this week to above 8.5m, nearing a record 8.91m seen in 2013, as rain continued in Hungary, Slovakia and Austria.

“According to forecasts, one of the biggest floods of the past years is approaching Budapest but we are prepared to tackle it,” said Budapest’s mayor, Gergely Karácsony.

Meanwhile, police in the Czech Republic said four people were missing on Sunday. Three had been in a car that was swept into a river in the north-eastern town of Lipová-lázne, while another man was missing after being swept away by floods in the south-east.

A dam in the south of the country burst its banks, flooding towns and villages downstream. “What you see here is worse than in 1997 and I don’t know what will happen because my house is under water and I don’t know if I will even return to it,” said Pavel Bily, a resident of Lipová-lázne.

On Saturday, four people died in floods in south-east Romania. In the worst-affected region, Galati in the south-east, 5,000 homes were damaged.

Romania’s president, Klaus Iohannis, said: “We are again facing the effects of climate change, which are increasingly present on the European continent, with dramatic consequences.”

Hundreds of people have been rescued across 19 parts of the country, emergency services said, releasing a video of flooded homes in a village by the Danube river.

“This is a catastrophe of epic proportions,” said Emil Dragomir, the mayor of Slobozia Conachi, a village in Galati where 700 homes had reportedly been flooded.

Slovakia has declared a state of emergency in the capital, Bratislava. Heavy rains are expected to continue until at least Monday in the Czech Republic and Poland.