Trump said he had directed US Vice President JD Vance, Secretary of State Marco Rubio, and top US military officer Dan Caine to work with the two countries "to achieve a Lasting PEACE."
"It has been my Honor to solve 9 Wars across the World, and this will be my 10th, so let''s, GET IT DONE!" said Trump, who launched the war on Iran alongside Israel on 28 February.
Hezbollah then pulled Lebanon into the Middle East war, firing rockets at Israel in support of its backer Tehran.
Since then, Israeli strikes on Lebanon have killed more than 2,000 people and displaced more than one million, and Israeli ground forces have invaded the country''s south.
Trump said late Wednesday that Aoun and Netanyahu were due to speak on Thursday, but there was no confirmation that any such call had happened.