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.
Trump, who 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.
The militaries of both Israel and Iran urged civilians on the opposing side to take precautions against further strikes on Sunday.
The Israeli military, which launched the attacks on Friday with the stated aim of wiping out Iran's nuclear and ballistic missile programs, warned Iranians living near weapons facilities to leave the area.
"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 where six people were killed in Bat Yam, a town south of Tel Aviv.
Iran's armed forces told residents of Israel to leave the vicinity of "vital areas" for their safety.
"Do not stay or travel near these critical areas," an Iranian armed forces spokesperson said in a video broadcast by state TV around the time that Iran sent a new barrage of missiles towards Israel.
Iran's health ministry said 224 people had been killed since Israel's attack began on Friday.
Spokesman Hossein Kermanpour said on social media that 1277 other people were hospitalised, and asserted that more than 90 per cent of the casualties were civilians.
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.
Explosions rattled Tel Aviv in the afternoon as Iran launched its first daylight missile raid since Israel attacked on Friday.
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.
The intelligence chief of Iran's Revolutionary Guards, Mohammad Kazemi, and his deputy were killed in Israel's attacks on Tehran on Sunday, the Iranian Tasnim news agency reported.
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.
An official said Israel still had a long list of targets in Iran and declined to say how long the offensive would continue.
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.
