"I'm told that President Trump has recently stated that he would like to end the war," said Leo, the first pontiff from the United States.
"Hopefully he's looking for an off-ramp," the Pope told journalists outside his residence in Castel Gandolfo, near Rome.
"Hopefully he's looking for a way to decrease the amount of violence."
Leo, who is known for choosing his words carefully, rarely makes direct appeals to leaders but he has been stepping up criticism of the Iran war in recent weeks.
On Sunday, the Pope - citing a passage from the Bible - said that God rejects the prayers of leaders who start wars and have "hands full of blood".
The month-long Iran conflict, started by joint US-Israeli air strikes on Iran on February 28, has spread across the region, killing thousands, disrupting energy supplies and threatening to send the global economy into a tailspin.
Leo lamented on Tuesday the number of people who have been killed and said he hoped the violence could end before Easter on April 5.
"There have been so many deaths, including innocent children," the Pope said.
"Let's continually appeal for peace."
"There are too many people who promote fighting, violence (and) war," Leo said.
Meanwhile, the Vatican announced on Tuesday that the Pope will carry the cross himself during the Good Friday procession at the Colosseum in Rome in remembrance of the Passion of Jesus Christ.
By doing so, the head of the Catholic Church is returning to a tradition of the Easter celebrations, it said.
This will be Leo's first Easter as pontiff.
His predecessor, Francis, died on Easter Monday last year at the age of 88.
Due to his failing health, the Argentinian was unable in his final years to take part in the Stations of the Cross, which is held at the Colosseum after dark.
Nevertheless, tens of thousands of worshippers regularly gathered at the almost 2000-year-old amphitheatre.
In 2020 and 2021, the ceremony had to be moved to St Peter's Square due to the COVID-19 pandemic.
Another Easter tradition is for the pontiff to wash the feet of the faithful on Holy Thursday.
Leo plans do this in Rome's Archbasilica of St John Lateran for 12 priests - unlike Francis, who had visited prisoners in jail for this purpose.
On Sunday, following Easter Sunday Mass in St Peter's Square, the Pope is expected to impart the Urbi et Orbi - Latin for to the city and the world - blessing before tens of thousands of people.
According to tradition, Jesus was sentenced to death and crucified on Good Friday.
The Stations of the Cross retrace the final stages of his suffering.
His resurrection is then celebrated on Easter Sunday.
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