The US ambassador to the Holy See Brian Burch said Rubio and the Pope would have "frank" discussions on Thursday.
"Nations have disagreements, and I think one of the ways that you work through those is ... through fraternity and authentic dialogue," Burch said.
Rubio and the Pope would "have a frank conversation about US policy, to engage in dialogue', he said.
Later in Washington, Rubio told reporters at the White House that he expected a discussion with Pope Leo on issues that would cover Cuba and concerns over religious freedom around the world.
"There's a lot to talk about with the Vatican," Rubio said.
"The Pope is obviously the vicar of Christ, is a Roman Catholic, but he's also the head of a nation state."
"We work with the Catholic Church on the distribution of humanitarian aid in Cuba. We share with the Catholic Church a concern about the destruction of religious liberty, the persecution of Christian minorities, and also, you know, the challenges that are being faced by Christians in Africa," he said.
Trump has repeatedly disparaged the first US-born Pope in recent weeks, drawing a backlash from Christian leaders across the political spectrum.
On Monday, Trump told right-wing radio talk show host Hugh Hewitt that "the Pope would rather talk about the fact that it's okay for Iran to have a nuclear weapon, and I don't think that's very good".
Leo has never said Iran should have nuclear weapons, but he has opposed the war which Trump says is aimed at ending Iran's nuclear program.
Tehran denies seeking nuclear weapons but says it has the right to develop nuclear technology for peaceful purposes, including enrichment, as a party to the Nuclear Non-Proliferation Treaty.
Responding to Trump's attack, Leo said he wanted to spread the Christian message by speaking about peace but that people were free to criticise him.
"The mission of the Church is to preach the Gospel, to preach peace," said the Pope.
"If someone wants to criticise me for preaching the Gospel ... I hope simply to be listened to because of the value of God's words."
Leo also firmly rejected the idea that he supported nuclear weapons, which the Catholic Church teaches are immoral.
"The Church has spoken out for years against all nuclear arms, on that there is no doubt," he said.
Rubio is Catholic, as is Vice President JD Vance. The two met Leo a year ago after attending his inaugural mass.
The Pope has also sharply criticised the Trump administration's hardline anti-immigration policies. And he has called for dialogue between the US and Catholic-majority Cuba, which has suffered frequent blackouts owing to US sanctions intended to put pressure on its one-party communist government.
