The big four -- House Speaker Nancy Pelosi, Senate Majority Leader Chuck Schumer, Republican Senate Leader Mitch McConnell and House Republican Leader Kevin McCarthy -- met behind closed doors with Zelenskyy ahead of his address to Congress.

Zelenskyy was spotted walking through Statuary Hall outside the House chamber with Pelosi, Schumer and McConnell, but McCarthy, the likely incoming House speaker, was not with them for that walk.

McCarthy, also needing to win over conservatives to back his bid for speaker, has signaled he could oppose more funding to Ukraine, warning that Republicans will not write a "blank check" for aid when they soon assume the majority.

Some conservative House Republicans have made it clear they would oppose any additional funding even as Congress votes on a must-pass $1.7 trillion government funding bill this week that includes $45 billion in aid to Ukraine.

-ABC News' Katherine Faulders and Lauren Peller

President Biden defended the decision to send a Patriot missile defense system to Ukraine and denied the move was escalatory.

"It's a defensive system. It's a defensive weapon system. It's not escalatory, it's defensive," Biden said. "We'd love to not have them use it. Just stop the attacks," he said, referring to Russia.

Zelenskyy delicately added that he may call on the U.S. to send another Patriot missile in the near future, prompting laughter.

"We're working on it," Biden said with a smile.

Zelenskyy said, "We are in war. I'm sorry. I'm really sorry. That is my appreciation."

The training of Ukrainian troops on the Patriot missile battery could take "several months," according to a senior defense official who briefed reporters this afternoon.

"I can just say that the training will begin very soon," the official said, noting the "Ukrainians will have to complete the training in order to be able to field the system and it's the Ukrainians who are operating the system."

The Patriot missile system and JDAM kits to convert "dumb bombs" to "smart bombs" are included in the latest round of military aid to Ukraine. Ukraine has been asking for the advanced air defense system since shortly after Russia's invasion began.

The official would not provide any concrete timelines, telling reporters: "We also would obviously want to be really, really careful for operational security reasons to not you know, not be overly precise on a date, even once we have it."

-ABC News' Luis Martinez

Zelenskyy was asked by a reporter what his message is to the American people ahead of his address to U.S. lawmakers later this evening.

"I think I will tell you very simple things which are very important for me," Zelenskyy responded. "And I think so that we have the same values and the same understanding of the life, the sense of the life. My message: I wish you peace."

"And I wish you to see your children alive and adult," Zelenskyy continued. "And I wish you to see your children when they will go to universities, and to see their children. I think that is the main thing, what I can wish you."

Zelenskyy said the U.S. and Ukraine are fighting for "common victory against this tyranny" and predicted, "We will win."

"I really want win together," he said, before slightly amending his words: "Not 'want.' Sorry. I'm sure."