Trump, who has said he is open to having a dialogue with Iran, has sought to downplay fears of military conflict, but the Iranians have said they have no interest in communicating with the White House.
Trump commented during a day that opened with the high pageantry of his meeting with Japan's emperor but quickly gave way to deliberations over thorny global issues, including North Korea, trade tensions with his Japanese host and the escalating friction between the US and Iran, according to Financial Tribune.
"I know that the prime minister and Japan have a very good relationship with Iran so we'll see what happens," he said while meeting with Abe in Tokyo, AP reported.
"The prime minister's already spoken to me about that and I do believe that Iran would like to talk. And if they'd like to talk, we'd like to talk also. We'll see what happens ... Nobody wants to see terrible things happen, especially me."
Trump has imposed tough new sanctions on Iran, which are severely affecting its economy. Late last week, he announced the deployment of 1,500 US troops to the region amid the tensions.
The US had earlier deployed an aircraft carrier and B-52 bombers to the Persian Gulf in response to the alleged intelligence of Iranian threats to US interests in the region.
Not Looking for Regime Change
Trump also said the United States is not looking for "regime change" in Iran, Aljazeera reported.
"We're not looking for regime change; we're looking for no nuclear weapons," Trump said at a joint press conference with Abe, adding that he believed "we'll make a deal" with Iran.
Tehran denies any military dimensions to its nuclear activities, stressing that the program is only meant for civilian uses such as power generation and medical applications.
Trump and Abe held talks after the US president became the first world leader to meet Japan's new emperor, Naruhito, who ascended to the throne on May 1.
The US president was the center of attention at a grand outdoor welcome ceremony at Japan's Imperial Palace, where he took a solo walk down red carpets, reviewing Japanese troops as the guest of honor.
The visit has been overshadowed by Trump’s threat to impose potentially devastating tariffs on Japan's auto industry.
He has suggested he will impose the levies if the US cannot win concessions from Japan. Japan's trade surplus surged almost 18% in April to 723 billion yen ($6.6 billion).
Trump said he wants to get "the balance of trade ... straightened out rapidly".
Trump also said he had a good feeling that the nuclear standoff with North Korea will be resolved.
"I may be right, I may be wrong. But I feel that we've come a long way. There's been no rocket testing, there's been no nuclear testing," he said.