WASHINGTON — President Zelensky will address Congress, the actor-turned-wartime leader’s latest video speech as he uses the West’s great legislative bodies as a global stage to orchestrate support against Russia’s crushing invasion.

Mr. Zelensky’s livestreamed address Wednesday into the Capitol will be among the most important in a unique and very public strategy in which he has invoked Winston Churchill, Hamlet and the power of world opinion in his fight to stop Russia.

Nearing the three-week mark in an ever-escalating war, Mr. Zelensky has used his campaign to implore allied leaders to “close the sky” to prevent the Russian airstrikes that are devastating his country. It’s a singular request and now a rallying cry in popular culture. 

It has also put Mr. Zelensky at odds with President Biden, whose administration has stopped short of providing a no-fly zone or the transfer of military jets from neighboring Poland as America seeks to avoid a direct confrontation with Russia.

Instead, Mr. Biden will deliver his own address following Mr. Zelensky’s speech, in which he is expected to announce an additional $800 million in security assistance to Ukraine, according to a White House official familiar with the matter. That would bring the total announced in the last week alone to $1 billion. It includes money for anti-armor and air-defense weapons, according to the official, who was not authorized to comment and spoke on the condition of anonymity.

Appearing in his now trademark army green T-shirt as he appeals to world leaders, the boyish but unshaven Mr. Zelensky has emerged as a heroic figure at the center of what many view as the biggest security threat to Europe since World War II. Almost 3 million refugees have fled Ukraine, the fastest exodus in modern times.

Invoking Shakespeare’s hero last week, he asked British lawmakers whether Ukraine is “to be or not to be.” On Tuesday, he appealed to “Dear Justin” as he addressed Canada’s parliament and Prime Minister Justin Trudeau. 

Mr. Zelensky called on European Union leaders at the start of the war to do the politically unthinkable and fast-track Ukraine’s membership — and he has continued to push for more help to save his young democracy than world leaders have so far pledged to do.

”I know he will ask for more help,” said Senator Warren.

Mr. Biden has insisted there will be no American troops on the ground in Ukraine and has resisted Mr. Zelensky’s relentless pleas for warplanes as too risky, potentially escalating into a direct confrontation with nuclear-armed Russia.

“Direct conflict between NATO and Russia is World War III,” Mr. Biden has said.

American defense officials, for their part, say they are puzzled by Mr. Zelensky’s demand for more warplanes. They say Ukraine isn’t often flying the planes it has now, while making good use of other weapons the West is providing, including Stinger missiles for shooting down helicopters and other aircraft.

While officials are anticipating that Mr. Zelensky may once again call on America and the West for fighter jets or help establishing a no-fly zone, the Biden administration is looking to send Ukraine “more of what’s been working well,” according to an official who was not authorized to comment and spoke on the condition of anonymity.

Already the Biden administration has sent Ukraine more than 600 Stinger missiles, 2,600 Javelin anti-armor systems, unmanned aerial system tracking radars; grenade launchers, 200 shotguns, 200 machine guns and nearly 40 million rounds of small arms ammunition, along with helicopters, patrol boats, satellite imagery and body armor, helmets, and other tactical gear, the official said.

Even though Messrs. Zelensky and Biden speak almost daily by phone, the Ukrainian president has found a potentially more receptive audience in Congress.

This won’t be the first time he has appealed directly to members of the House and Senate, who have remained remarkably unified in their support of Ukraine with some feeling they have made a commitment to do as much as they can in the fight against Russia. Nearly two weeks ago, Mr. Zelensky delivered a desperate plea to some 300 lawmakers and staff on a private call that if they could not enforce a no-fly zone, at least send more planes.

“We think the United States needs to do more,” said Senator Wicker, a Mississippi Republican, returning from a weekend visit with other lawmakers to Poland.

Congress has already approved $13.6 billion in military and humanitarian aid for Ukraine, and the newly announced security aid will come from that allotment, which is part of a broader bill that Mr. Biden signed into law Tuesday. But lawmakers expect more aid will be needed.

Speaker Pelosi said Mr. Zelensky asked for help in rebuilding his country when they spoke last week.

It was in that call that Mr. Zelensky asked for the opportunity to address Congress, something the Democratic leader readily agreed to.

“The Congress, our country and the world are in awe of the people of Ukraine,” said Ms. Pelosi and Senator Schumer in a statement Monday announcing the address.

They said Congress “remains unwavering in our commitment to supporting Ukraine as they face Putin’s cruel and diabolical aggression.”