Trump comments come in advance of Sunday's presidential election in France, a contest that has high stakes for the future of the European Union.
Of the new health care bill being negotiated by House Republican leaders, the president said, "This is a great bill". He did not specifically weigh in on the French election.
Trump also voiced optimism that the USA had successfully enlisted China to try to persuade North Korea to give up its nuclear weapons program.
Trump has pulled the United States out of the Trans-Pacific Partnership, a pact he said was "a disaster".
"I do not see a role in Libya", Trump stated.
Libya descended into chaos with a civil war in 2011 that ended with the killing of longtime leader Moammar Gadhafi (MOO'-ah-mar gah-DAH'-fee).
Like Mr. Trump, Gentiloni is also new to his office, taking the post in December.
Trump plans to attend a North Atlantic Treaty Organisation meeting in Belgium next month before the Group of Seven gathering in Italy.
Weeks before President Donald Trump's first official overseas trip, trade and security matters were top items of discussion going into his meeting Thursday with the prime minister of Italy, one of the two European countries set to welcome Trump in May.
White House spokesman Sean Spicer said Wednesday that the White House would be reaching out to the Vatican to "see if a meeting, an audience with the Pope can be accommodated".
President Donald Trump is holding his first meeting with Italy's prime minister. "The plan gets better and better, and it's gotten really good".
And, with a funding deadline looming to keep the government running, Trump said it was possible Congress would manage to accomplish it all next week or "shortly thereafter". "It shouldn't have been signed". Earlier this week, the administration certified to Congress than Iran was complying - at least technically - with the terms of the deal, clearing the way for Iran to continue enjoying sanctions relief in the near term. "It looks like another terrorist attack".
Paris police say a gunman has killed a police officer and wounded another before being killed himself in an attack on the Champs-Elysees shopping district. While disparaging the nuclear deal and accusing Iran of fomenting violence and terrorism throughout the Middle East, Trump has avoided committing to abandoning the agreement, a move that would be staunchly opposed by USA businesses and European allies.