US President Joe Biden has assured his Ukrainian counterpart that $60bn in military aid is on its way.
The measure still needs to pass a final congressional vote, but Mr Biden told Volodymyr Zelensky that he was confident it would be approved.
Mr Zelensky had earlier made an urgent appeal for more weapons to avoid a “catastrophic” situation in Europe.
The US has blamed Ukraine’s withdrawal from the battle at Avdiivka on a lack of Congressional support.
Earlier this week, the US Senate approved a $95bn (£75bn) foreign aid package – which includes $60bn for Ukraine – after months of political wrangling. But it still faces an uphill battle in the House of Representatives, where members of the Republican Party are divided on the measure.