"Nations have disagreements, and I think one of the ways that you work through those is ... through fraternity and authentic dialogue," said Brian Burch, the US ambassador to the Holy See.
"I think the secretary is coming here in that spirit," Burch told journalists.
"To have a frank conversation about US policy, to engage in dialogue."
Trump has repeatedly disparaged the first US-born pope in recent weeks, drawing a backlash from Christian leaders across the political spectrum.
In his latest comments, Trump told right-wing radio talk show host Hugh Hewitt that "the Pope would rather talk about the fact that it's OK for Iran to have a nuclear weapon, and I don't think that's very good".
"I think he's endangering a lot of Catholics and a lot of people. But I guess if it's up to the Pope, he thinks it's just fine for Iran to have a nuclear weapon," Trump said.
Leo has never said Iran should have nuclear weapons, but has opposed the war that Trump says is aimed at ending Iran's nuclear program.
Rubio is a Catholic, as is Vice-President JD Vance.
The two met Leo a year ago after attending his inaugural mass, the Trump administration's only previous known cabinet-level meetings with the Pope.
Burch was asked after an event hosted by his embassy at Rome's Gregorian University on Tuesday if Rubio was hoping to repair the relationship between Trump and Leo.
"I don't accept the idea that somehow there's some deep rift," the ambassador responded.
Rubio was going, Burch said, so the US and the Vatican could "better understand each other, and to work through, if there are differences, certainly to talk through that".
Rubio is also set to meet in Rome on Friday with Italian Prime Minister Giorgia Meloni, who defended the Pope.
Her defence minister has said the war in Iran puts US leadership at risk.
Leo, who marks his first year as leader of the 1.4-billion-member Catholic Church on Friday, maintained a relatively low profile on the global stage in the first months of his papacy but has emerged in recent weeks as a firm critic of the US-Israeli war on Iran.
The Pope has also sharply criticised the Trump administration's hardline anti-immigration policies and called for dialogue between the US and Catholic-majority Cuba to prevent violence.
