The appeal comes with both sides launching a fresh round of talks amid deadly air strikes in the capital Kyiv, nearly three weeks after Russia's President Vladimir Putin ordered the attack.
"We look forward to the privilege of welcoming President (Volodymyr) Zelensky's address to the House and Senate and to convey our support to the people of Ukraine as they bravely defend democracy," House leader Nancy Pelosi and her Senate counterpart Chuck Schumer said in a joint letter to lawmakers.
Anthony Rota, the Speaker of the Canadian House of Commons, said Zelensky would also address lawmakers in Ottawa, on Tuesday.
Zelensky's pleas for help to defend his country from Russia's deadly assault have grown increasingly desperate, and he has repeatedly urged Washington, the European Union and NATO for military hardware.
Dressed in a military-green T-shirt and seated beside a Ukrainian flag, Zelensky spoke to lawmakers from the US Republican and Democratic parties in a March 5 video call to plead for Russian-made planes.
Poland has offered to send Soviet-style MiG-29 fighter jets to Ukraine via a US air base in Germany.
The White House -- fearing the move could escalate tensions with Russia -- has rejected the proposal, saying it raised "serious concerns" for the entire NATO alliance.
And Moscow confirmed at the weekend that its troops could target supplies of Western weapons in Ukraine and that the pouring in of arms would turn convoys "into legitimate targets."
There is a growing clamor on both sides of Congress, however, for a more assertive US posture.
'Fighting chance'
"What we've heard directly from the Ukrainians is they want them badly," Republican Senator Rob Portman said of the planes in an interview with CNN Sunday during a trip to the Ukraine-Poland border.
"They want the ability to have better control over the skies in order to give them a fighting chance. I don't understand why we’re not doing it."
Democratic Senator Amy Klobuchar, who was also on the visit, told the network she had spoken to Biden "about 10 days ago" about the fighters, adding: "I'd like to see the planes over there."
Republicans initially led calls for the transfer last week, although military veterans among the Democrats and the 58-member bipartisan Problem Solvers Caucus have also backed the move.
"With Russia's alarming disregard for Ukrainian civilian casualties, the US must... help supply more comprehensive air defense systems to defend Ukraine and its people," they said in a letter of support.
Congress usually defers to the White House on foreign policy but has increasingly been pressuring the Biden administration for a more punitive response to Russia's aggression, with notable success.
Members of both parties called for tougher sanctions against Russia and authorized more than double the military and humanitarian aid the administration had requested for Ukraine.
Congress was also seen as having nudged Biden to announce a US ban on Russian oil, seen as politically risky amid spiraling gas prices, and led the pressure for Washington to end permanent normal trade relations with Russia.
Biden authorized $200 million in additional military equipment for Ukraine Saturday, on top of $350 million green-lit on February 26.
