Smoke rose over the Lebanese capital, and the Civil Defence said it retrieved three bodies and six wounded people from the rubble.
Iran threatened a military response.
Trump reacted on social media: "We are very close to a Deal that will bring peace to the region".
"Let's not blow it!" he said.
The deal in its current form is a deep disappointment to Israel's government, which has been sidelined in negotiations led by Pakistan and others.
The last time Israel struck the Beirut suburbs a week ago, it set off the most serious escalation of fighting between Iran and Israel since the tenuous ceasefire took hold on April 7.
Trump, who had said the deal could be signed on Sunday, has pressed Israeli Prime Minister Benjamin Netanyahu to stop hitting Lebanon hard while a deal is near, but the prime minister has defied him.
Netanyahu's office said the strikes were in response to Hezbollah attacks on northern Israel.
Israel's military said Hezbollah launched three projectiles, releasing footage where an audible boom was followed by rising smoke. There was no immediate comment from the Iranian-backed Hezbollah.
"Israel will not tolerate firing into its territory," Netanyahu and Defence Minister Israel Katz said in a statement. The military later said it was preparing for potential incoming fire in the coming hours.
An Associated Press photographer at the scene in Beirut said a five-story apartment building with shops on the ground floor was struck.
The two lowest floors were the most heavily damaged. Residents of the southern suburbs, many of whom had returned home after weeks of relative calm, could be seen fleeing.
Hezbollah fired missiles into Israel on March 2, two days after the US and Israel attacked Iran, sparking war in the Middle East.
Israeli troops have since pushed their invasion of Lebanon deeper than at any point in over a quarter century.
Iran wants a ceasefire deal to include the fighting in Lebanon.
Iran's parliamentary Speaker Mohammad Bagher Qalibaf, a lead negotiator for Tehran, warned the US on X after Israel's strikes that "if you lack the will and ability to fulfil your commitments, speaking of continuing the path is not possible".
"Without a doubt, these crimes will not go unanswered," said General Mohammad Jafar Asadi, deputy commander of Iran's Joint Command Headquarters, the official Mizan news agency reported.
Qatari mediators travelled to Tehran on Sunday to finalise the agreement, according to two regional officials.
The officials, who spoke on condition of anonymity because they were not authorised to speak to the media, expressed cautious optimism that the US and Iran were finally approaching a deal that could halt hostilities that have killed thousands of people and reopen the Strait of Hormuz, whose closure has thrown world markets into disarray.
Pakistani Prime Minister Shehbaz Sharif said Saturday the deal would be signed on Sunday, while Iran's foreign ministry spokesperson Esmail Baghaei said it could happen in the coming days.
Trump said the Strait of Hormuz would open immediately after the signing.
The deal is expected to be signed electronically, without an in-person ceremony, though it's unclear when or how the signing will take place.
The deal does not solve the thorniest issues between the US and Iran, including Iran's nuclear program or its billions of dollars in frozen funds, but offers a 60-day framework for technical discussions on those issues, according to Pakistani and regional officials familiar with the ongoing negotiations.
Iran has 440.9 kilograms of uranium that is enriched up to 60 per cent purity, a short, technical step from weapons-grade levels of 90 per cent, according to the International Atomic Energy Agency.
