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.
"Ukraine's military was forced to withdraw from Avdiivka after Ukrainian soldiers had to ration ammunition due to dwindling supplies as a result of congressional inaction," a White House statement read.
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.
"Look, the Ukrainian people have fought so bravely and heroically, they've put so much on the line and the idea that now, when they're running out of ammunition, we'd walk away - I find it absurd," Mr Biden told reporters following his call with Mr Zelensky on Saturday.
"I find it unethical, I find it just contrary to everything we are as a country", he added. "So I'm going to fight until we get them the ammunition they need and the capacity they need to defend themselves."
The Ukrainian president also urged US lawmakers to approve the financial package.
"I am glad that I can count on the full support of the American president," he posted on Telegram.
Mr Zelensky has been in Germany, where he made an urgent appeal for more weapons to avoid a "catastrophic" situation in Europe.
"Keeping Ukraine in the artificial deficits of weapons, particularly in deficit of artillery and long-range capabilities allows Putin to adapt to the current intensity of the war," he told an international conference in Munich.
"Ukrainians have proven that we can force Russia to retreat," he said. "We can get our land back."
"Do not ask Ukraine when the war will end. Ask yourself, why is Putin still able to continue it?"
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.
"If you can't count on your partner, because America was saying you can count on us, we will be with Ukraine as long as it takes, and where are those words now?" he said.
"We're dying every day."
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.
"The Russian city of Avdiivka, one of the oldest settlements in Donbas, today returned home to Russia," he said in a video posted on Telegram.
"On behalf of all residents of Donbas, I sincerely thank Russian military personnel, our army, our president, for the fact that the Donetsk People's Republic continues to be liberated."
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".
"Our soldiers performed their military duty with dignity, did everything possible to destroy the best Russian military units, inflicted significant losses on the enemy in terms of manpower and equipment," he said.
Source: BBC
