The leaders met for a summit on Lake Geneva in France while details of the US-Iran ceasefire agreement trickled out of Washington and Tehran before its expected unveiling on Friday across the nearby Swiss border.
The US-Iran agreement will launch negotiations towards a final settlement to end the war, which has killed more than 7000 people, mostly in Iran and Lebanon.
"We underline the need for the negotiation ... to address the threats posed by Iran in the region and beyond and ensure that they never obtain a nuclear weapon," the leaders said in a statement on Wednesday.
The summit gave US President Donald Trump a chance to present his deal with Iran to major allies Britain, Canada, France, Germany, Italy and Japan.
The leaders said they were ready to contribute to the implementation of the accord, with a coalition led by Britain and France set to help secure shipping once the Strait of Hormuz reopens as expected on Friday.
The memorandum of understanding signed by Washington and Tehran on Monday, though yet to be made public, extends a ceasefire announced in April by another 60 days to allow the warring countries to negotiate a permanent truce.
The US president appears to have achieved little of what he said he wanted at the outset of the war.
Iran's theocratic government remains in place, its stockpile of highly enriched uranium has not been surrendered, its ballistic missile capabilities have not been destroyed and it has not ended its support for anti-Israel militias such as Hezbollah in Lebanon.
Trump said the agreement stated that Iran would not have a nuclear weapon - a restatement of Iran's official position since the 1970s - and US officials say further discussions will lead to the removal or destruction of its enriched uranium stockpile.
One of the biggest questions still hanging over the truce is the fate of Lebanon, which Israel invaded in March to root out Hezbollah after the militant group fired across the border in solidarity with Tehran following US-Israeli strikes on Iran.
Israeli forces still occupy a swathe of southern Lebanon, where more than a million people have been driven from their homes, while Hezbollah remains undefeated.
Iran says the ceasefire must also end hostilities in Lebanon, and that a permanent deal must lead to an Israeli withdrawal.
Israel, which was excluded from the US-Iran peace negotiations, says it will not withdraw and reserves the right to use military force.
That has opened up a rift between Israel and the United States, with Trump publicly berating his wartime ally Israeli Prime Minister Benjamin Netanyahu, saying he was "not happy" with the way Israel had handled itself.
"Without us, without the United States, there would be no Israel. Without me, there would be no Israel, because no other president was willing to do what I did," Trump said.
In their statement, the G7 leaders called for an "immediate robust ceasefire" in Lebanon and the disarmament of Hezbollah.
After decades of US and international sanctions on Iran, a peace deal could deliver economic benefits, with the memorandum including a $US300 billion ($A424 billion) reconstruction fund, paid for by neighbouring Gulf states, if Iran complies with other terms.
A senior US official said the US would also waive sanctions on Iranian oil.
In the coming 60 days, negotiators will return to difficult issues such as the future of Iran's nuclear program.
But Iran's support for regional militia groups and its missile arsenal do not appear to be on the agenda, in what would amount to major US concessions.
The G7 leaders said they had committed to "accelerate the diversification of energy supply routes in order to reduce global vulnerability to the Strait of Hormuz and to increase our energy stocks".
