The Ukrainian president, Volodymyr Zelenskiy, will deliver a virtual address to the US Congress on Wednesday, the latest in a series of speeches to western leaders as he works to galvanize support for his besieged nation.

The remarks to both chambers of Congress come on day 21 of the battle for Ukraine’s survival under an intensifying assault from Russia.

Russian troops are advancing on the Ukrainian capital, Kyiv, in a war that has already killed hundreds of civilians in aerial and artillery bombardment, including at least 100 children.

More than 3 million people have fled Ukraine since the invasion, causing the fastest-growing refugee crisis in Europe since the second world war.

Zelenskiy’s speech follows similar addresses to the UK parliament, in which he invoked Shakespeare and echoed Winston Churchill’s famous wartime oration to the House of Commons about defiance in the face of an apparently overwhelming aggressor.

On Tuesday, Zelenskiy appealed to Canada’s parliament, and the nation’s large Ukrainian diaspora, to rally behind his country. That evening, the prime ministers of Nato allies and Russian neighbors Poland, the Czech Republic and Slovenia traveled by train to Kyiv, which was under a 35-hour curfew as Russian shells and missiles rained down on the capital, striking residential areas and civilian infrastructure.

It came on the same day Zelenskiy acknowledged that Ukraine’s longstanding hope of joining Nato was unlikely.

“For years, we heard about the apparently open door, but have already also heard that we will not enter there, and these are truths and must be acknowledged,” the Ukrainian president said in a speech before the leaders of the Joint Expeditionary Force, a UK-led initiative bringing together 10 north Atlantic countries to create a capability for responding rapidly to crises.

In his remarks on Wednesday, which will come nearly two weeks after Zelenskiy met virtually, behind the scenes, with a small group of members of Congress, he is expected to call on the US once again to “close the skies” over Ukraine.

He is also likely to press to be supplied with fighter jets by Nato allies that Ukrainian pilots can fly up against Russian air forces, and steeper economic sanctions in the face of an advancing Russian assault.

The Biden administration has so far flatly ruled out an option of the west imposing a no-fly zone over the country, determined to avoid inevitable direct combat between the US and Russian forces – a conflict the US president has said would lead to “world war three”.

The Biden administration also rejected an offer from Poland to turn over its Soviet-era fighter jets to Ukraine, which had been made only if the US and Nato facilitated the transfer. Administration officials argued the move could be seen as escalatory by Moscow.

But Biden is facing growing pressure to reconsider his position. A growing chorus of lawmakers on Capitol Hill are publicly pressuring Biden to increase military aid to Ukraine, including sending fighter jets and air defense systems.

The calls come as the US and allies tighten their economic vice on Russia, apparently leading Moscow to turn to China for financial support.

On Tuesday, Biden signed into law a funding measure that will provide a record $13.6bn in emergency aid to Ukraine and its European allies.

This week, lawmakers are expected to take up legislation that would end normal trade relations with Russia after Biden last Friday said the US would join Europe and other allies in revoking its preferred trade status.

Biden will travel to the Belgian capital, Brussels, next week for a meeting with Nato leaders to discuss the ongoing crisis in Ukraine and reassure allies of the US’s commitment to the defense alliance.

“His goal is to meet in person, face-to-face with his European counterparts and talk about where we are at this point in the conflict in the invasion of Ukraine by Russia,” the White House press secretary, Jen Psaki, said on Tuesday.

She added: “We’ve been incredibly aligned to date – that doesn’t happen by accident. The president is a big believer in face-to-face diplomacy, so it’s an opportunity to do exactly that.”