Israel and Iran launched fresh attacks on each other overnight into Sunday, killing scores.
"Iran and Israel should make a deal, and will make a deal," Trump said on Truth Social, adding that "we will have PEACE, soon".
"Many calls and meetings now taking place," he said.
Trump did not offer any details about the meetings or evidence of progress toward peace.
His assertion contradicted comments by Prime Minister Benjamin Netanyahu, who said on Saturday that Israel's campaign against Iran would intensify.
A White House spokeswoman did not immediately respond to a request for comment on how Trump and the White House were working to de-escalate the situation in the Middle East.
Trump, who portrays himself as a peacemaker and has drawn criticism from many of his supporters for not being able to prevent the Israel-Iran conflict, cited other disputes that he took responsibility for solving, including between India and Pakistan, and lamented not getting more praise for doing so.
"I do a lot, and never get credit for anything, but that's OK, the PEOPLE understand. MAKE THE MIDDLE EAST GREAT AGAIN!" he wrote.
Israeli rescue teams combed through rubble of residential buildings destroyed by Iranian missiles on Sunday, using sniffer dogs and heavy excavators to look for survivors after at least 10 people, including children, were killed, raising the two-day toll to 13.
Sirens rang out across Israel after 4pm in the first such daylight alert, and fresh explosions could be heard in Tel Aviv.
In Iran, images from the capital Tehran showed the night sky lit up by a huge blaze at a fuel depot after Israel began strikes against Iran's oil and gas sector - raising the stakes for the global economy and the functioning of the Iranian state.
Iranian authorities have not given a full death toll but said 78 people were killed on Friday and scores more have died since, including in a single attack that killed 60 on Saturday, half of them children, in a 14-storey apartment block flattened in Tehran.
At least 14 Iranian nuclear scientists have been killed in Israeli attacks since Friday, including in car bombs, two sources in the Gulf said on Sunday.
Israel launched "Operation Rising Lion" with a surprise attack on Friday morning that wiped out the top echelon of Iran's military command and damaged its nuclear sites, and says the campaign will continue to escalate in coming days.
Iran has vowed to "open the gates of hell" in retaliation.
The Israeli military warned Iranians living near weapons facilities to leave.
"Iran will pay a heavy price for the murder of civilians, women and children," Israeli Prime Minister Benjamin Netanyahu said from a balcony overlooking blown-out apartments in the town of Bat Yam where six people were killed.
An official said Israel still had a long list of targets in Iran and declined to say how long the offensive would continue.
Those attacked on Saturday evening included two "dual-use" fuel sites that supported military and nuclear operations, he said.
Iranian President Masoud Pezeshkian said Iran's responses will grow "more decisive and severe" if Israel's hostile actions continue.
Two US officials told Reuters on Sunday Trump vetoed an Israeli plan to kill Iran's Supreme Leader Ayatollah Ali Khamenei.
"Have the Iranians killed an American yet? No. Until they do we're not even talking about going after the political leadership," said one of the sources, a senior US administration official.
The officials, speaking on condition of anonymity, said top US officials have been in constant communications with Israeli officials in the days since Israel launched its attack.
They said Israeli officials reported that they had an opportunity to kill Khamenei but Trump waved them off of the plan.
