US President Donald Trump said on Wednesday he hopes to meet Iran's supreme leader Mojtaba Khamenei, as Washington and Tehran accuse each other of violating an increasingly fragile ceasefire.

Mojtaba Khamenei, 56, is thought to have been wounded in US-Israeli strikes that killed his father, Ali Khamenei, and has not been seen in public since he was named his successor.

"I would like to meet him, and we probably will meet at some point, depending on how it all works out," the US president told the New York Post's "Pod Force One" podcast.

Trump added that Khamenei was "involved, absolutely" when asked about the Iranian cleric's health.

Khamenei involved in war talks: Trump, Rubio

"They say he is giving approval," Trump said. US Secretary of State Marco Rubio told a Congressional panel on Tuesday that Mojtaba Khamenei is alive and increasingly active.

"I think there are indications out there that he is increasingly engaging at some level," Rubio told the Senate Foreign Relations Committee.

An Iranian attack on Wednesday on Kuwait's airport marked one of the more severe tests yet of a shaky April 8 ceasefire.

Iran's Revolutionary Guards claimed the attack, which it said was in retaliation for US attacks on an Iranian oil tanker and island.