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.
Taking Avdiivka – a gateway to the Russian-seized Donetsk regional capital in the east – is Russia’s first notable gain since they seized nearby Bakhmut in May.
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.
The Ukrainian president also urged US lawmakers to approve the financial package.
Mr Zelensky has been in Germany, where he made an urgent appeal for more weapons to avoid a “catastrophic” situation in Europe.
Ukraine is critically dependent on weapons supplies from the US and other Western allies to keep fighting Russia – a much bigger military force with an abundance of artillery ammunition.
UK Foreign Secretary David Cameron said help for Ukraine from the UK, the EU and the US would make a “real difference” to the fight against Russia.
Speaking to the BBC, Ukrainian MP Oleksiy Goncharenko said that he felt let down by the American leadership.
Avdiivka has been engulfed in fierce fighting for months and has been a battlefield town since 2014, when Russian-backed fighters seized large swathes of the eastern Donetsk and Luhansk regions.
The fall of Avdiivka marks the biggest change on the more than 1,000km-long (620-mile) front line since Russian troops seized the nearby town of Bakhmut in May 2023.
The head of the self-proclaimed Donetsk People’s Republic, Denis Pushilin, welcomed Russia’s territorial gain.
Announcing the decision to withdraw early on Saturday, head of the Ukrainian armed forces Gen Oleksandr Syrskyi said he acted “to avoid encirclement and preserve the lives and health of service personnel”.
