Blinken travelled to Warsaw on Thursday after spending a day in Kyiv with British Foreign Secretary David Lammy during which they pledged to bring the Ukrainian requests to their leaders.
President Joe Biden and British Prime Minister Keir Starmer are to meet in the United States on Friday amid signs both Washington and London are growing more receptive to allowing the Ukrainians to use their arms to hit targets farther inside Russia than previously approved.
NATO member Poland, which shares a border with Ukraine, has been supportive of the Ukrainians and Blinken is likely to hear further requests for easing weapons-use restrictions from Polish President Andrzej Duda, Prime Minister Donald Tusk and Foreign Minister Radosław Sikorski.
On Wednesday, Blinken and Lammy announced the United States and Britain had pledged nearly $US1.5 billion ($A2.2 billion) in additional aid to Ukraine during their visit to Kyiv.
Antony Blinken and UK counterpart David Lammy promised more aid to President Volodymyr Zelenskiy. (AP PHOTO)
Blinken announced more than $US700 million in humanitarian aid, while Lammy confirmed his country would provide another $US782 million in assistance and loan guarantees.
Much of the effort was aimed at bolstering the energy grid that Russia has repeatedly pounded before an expected difficult winter.
Ukraine's wish list is long and non-military assistance is certainly on it, but Ukrainian officials made clear their most important ask is for easing restrictions on where Western weapons can be used.
Blinken said he would bring the discussion with Ukrainian President Volodymyr Zelenskiy about the missiles "back to Washington to brief the president", and Biden and Starmer would "no doubt" talk about the issue in Washington.
Biden's language was very similar to that which he used in May, shortly before the US green-lit Ukrainian use of US weapons just inside Russian territory.
The diplomatic visit unfolded as Russia's bigger and better-equipped army bears down on Ukraine's eastern Donetsk region and conducts aerial attacks on cities across the country using missiles, glide bombs and drones that claim many civilian casualties.
But relations between Ukraine and its Western partners have been increasingly strained by Kyiv's repeated appeals for the West's authorisation to use long-range weapons from the United States and other allies to strike targets deeper inside Russia.
That issue took on added urgency after Russia's latest reported acquisition of ballistic missiles from Iran, but Western leaders have so far baulked at Ukraine's request, fearing that, if granted, it could escalate the war.
Biden has allowed Ukraine to fire US-provided missiles across the border into Russia in self-defence, but has largely limited the distance they can be fired.
Zelenskiy said he hoped for changes to those limitations.
"Let's count on some strong decisions, at least," he said.
"For us, it's very important."
