Meeting days after a suicide bomber killed 22 people at a concert in northern England, the leaders did issue a joint statement on fighting terrorism, admonishing internet service providers and social media companies to "substantially increase" their efforts to rein in extremist content.
Host Paolo Gentiloni, the prime minister of Italy, said the group was also inching closer to finding common language on trade, a contentious issue between Trump - elected on an "America First" platform - and the six other leaders.
But on the issue of climate, there was no breakthrough.
"There is one open question, which is the U.S. position on the Paris climate accords," Gentiloni told reporters, referring to a 2015 deal on reducing greenhouse gas emissions. "All others have confirmed their total agreement on the accord."
U.S. officials had signalled beforehand that Trump, who dismissed climate change as a "hoax" during his campaign, would not take a decision on the climate deal in Taormina, the cliff-top town overlooking the Mediterranean where G7 leaders met.
But other leaders, including German Chancellor Angela Merkel and new French President Emmanuel Macron, had hoped to sway the president at his first major international summit since entering the White House four months ago.
Merkel described the climate debate as "controversial". There was a "very intensive" exchange of views, she said.
Trump's economic adviser Gary Cohn said Trump's views on climate were "evolving" and that he would ultimately do what was best for the United States.
The summit, held at a luxury hotel that was once a Dominican monastery and base for the Nazi air force during World War Two, took place a day after Trump blasted NATO allies for spending too little on defence and described Germany's trade surplus as "very bad" in a meeting with EU officials.
His NATO speech shocked allies, who had been expecting him to reaffirm Washington's commitment to Article 5, the part of the military alliance's founding treaty which describes an attack on one member as an attack on all.
They were also disappointed that he did not touch on Russia, which was expelled from what was then called the G8 in 2014 because of its annexation of Crimea from Ukraine.
Accusations from U.S. intelligence agencies that Russia intervened in the U.S. election to help Trump, and investigations into his campaign's contacts with Russian officials, have dogged his presidency and prevented him from delivering on a campaign promise to get close to Moscow.
The summit kicked off with a ceremony at an ancient Greek theatre overlooking the sea, where war ships patrolled the sparkling blue waters.
Nine fighter jets soared into the sky above Taormina, leaving a trail of smoke in the red-white-green colours of the Italian flag.
Italy chose to stage the summit in Sicily to draw attention to Africa, which is 140 miles (225 km) from the island at its closest point across the Mediterranean.
More than half a million migrants, most from sub-Saharan Africa, have reached Italy by boat since 2014, taking advantage of the chaos in Libya to launch their perilous crossings.
The deadly attack in Manchester was carried out by a suspected Islamist militant of Libyan descent who grew up in Britain.
"Today G7 leaders have joined Britain in condemning this barbaric act of violence," said British Prime Minister Theresa May, who left the summit a day early to deal with the aftermath of the attack.
Speaking about internet companies, she added: "In particular, I want to see them report this vile content to the authorities and block the users who spread it."
The leaders are expected to issue a final communique on Saturday. Italian officials have suggested it will be shorter than 10 pages, compared to 32 pages at the last G7 summit in Japan.
As the leaders attended a concert and gala dinner, aides continued to work on the final wording.
"On the major theme of global trade, we are still working on the shape of the final communique, but it seems to me the direct discussions today have produced common positions that we can work on," said Gentiloni.
(Writing by Noah Barkin; Additional reporting by Crispian Balmer, John Irish, Andreas Rinke, Giselda Vagnoni, Steve Scherer, Elizabeth Piper; Editing by Alison Williams)
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)