The Vistula River, which flows for 1,050 kilometres from the mountainous south to the Baltic Sea in the north, has been bursting its banks and submerging homes and roads.
Michal Boni, chief aide to Tusk, said 23,000 people had been evacuated from flood-hit areas and 100,000 had been affected in total.
The water level rose to levels reached only three other times in the past sixty years. Authorities urged residents of riverside districts to keep alert.
"The flood-wave is longer than expected and could keep passing through the capital until Sunday evening," regional governer Jacek Kozlowski told reporters.
"We're not worried about the river actually overflowing, but the dykes will be sodden for so long that they risk bursting at any moment," he said.
An EU emergency operation was launched on Wednesday, after a request from the Polish government.
By Friday, rescuers and equipment had been sent from France, Germany, Lithuania, Latvia and Estonia. Aid also arrived from the neighbouring Czech Republic, which has been affected by the floods.
If the cost of flood damage is found to have exceeded 2.1 billion euros, Poland can request help from an EU crises fund, unlocking 100 million euros.