Biden addresses his age, Taylor Swift conspiracies and more on Seth Meyers' late-night show

President Joe Biden, while campaigning in New York, stopped by 30 Rockefeller Plaza to appear on NBC's "Late Night With Seth Meyers."

The president's sit-down with the comic late Monday included questions about his age and his 2024 agenda versus that of former President Donald Trump, the Republican front-runner for the nomination.

"Some documents recently leaked, some classified documents -- and this isn't a gotcha show but I do want to ask about it -- that says you are currently 81 years old," Meyers began.

"Who the hell told you that?" Biden joked. "That's classified."

Meyers then turned to a more serious note, highlighting the fact that polls show voters are concerned about Biden's age as he runs for a second term and asking how Biden plans to address that on the campaign trail.

"No. 1, you got to take a look at the other guy, he's about as old as I am," Biden said, swiping at Trump, who is 77.

"No. 2, it's about how old your ideas are," Biden continued. "Look, I mean, this is a guy who wants to take us back. He wants to take us back on Roe v. Wade. He wants to take us back on a whole range of issues that for 50, 60 years they've been solid American positions."

"I think it's about the future," Biden said. "And everything, every single thing we've done, and I think we've got some good things done … they told us we couldn't get them done, because things were so divided."

The interview comes as Biden (who has largely eschewed traditional press conferences or press interviews) seeks to tamp down voter worries and Republican criticisms about his age and stamina by ramping up his appearances. The choice of venue was also curated for an important demographic: younger voters.

In another moment of levity, Biden joked about conspiracy theories about Taylor Swift scheming with Democrats when it comes to everything from the Super Bowl to the 2024 election.

"Where are you getting this information?" Biden quipped when Meyers broached the subject. "It's classified."

Meyers also questioned Biden on Republicans holding up aid to Ukraine, Trump's "dictator" remarks and the Israel-Hamas conflict.

Biden, facing criticism by some Arab and Muslim communities in Michigan and elsewhere for his position on the Israel-Hamas war, said he believed there is a path forward -- albeit a "difficult" one -- on a cease-fire and hostage release.

"Ramadan is coming up and there's been an agreement by the Israelis that they would not engage in activities during Ramadan as well, in order to give us time to get all the hostages out," he said.

Earlier in the day, at an ice cream shop with Meyers, Biden said his hope is that there will be a cease-fire reached by next Monday -- comments that a senior Israeli source told ABC News caught Prime Minister Benjamin Netanyahu by surprise.

On his late-night appearance, Biden said without Israel, no Jewish person would be safe -- but also warned of diminished support for the country if it continues its current tactics in Gaza.

"Israel has had the overwhelming support of the vast majority of nations. If it keeps this up without this incredibly conservative government they have ... they're going to lose support from around the world," he said. "And that is not in Israel's interest."

ABC News' Lauren Minore contributed to this report.