The gathering in Italy is being billed as a key test of how serious the new US administration is about implementing its policy agenda, particularly on climate change.
G7 leaders met Friday with divisions on trade and climate change, and fresh friction surrounding US President Donald Trump, threatening to undermine a show of unity against terrorism.
"There is no doubt that this will be the most challenging G7 summit in years," European Union president Donald Tusk predicted, setting the tone for the two-day meet in Sicily's ancient hilltop resort of Taormina.
TRT World's Francis Collings reports from Siciliy.
The meeting comes days after children were among 22 people killed in a concert bomb attack in Manchester.
British Prime Minister Theresa May was to lead a discussion on terrorism with her aides saying she would issue a call for G7 countries to put more pressure on internet companies to ensure extremist content is quickly taken offline and notified to authorities.
United against terror
President Emmanuel Macron on Friday vowed France's total support for Britain's fight against terrorism after the Manchester attack as he met May at the G7 summit.
"We will be here to cooperate and do everything we can in order to increase this cooperation at the European level, in order to do more from a bilateral point of view against terrorism," Macron told her, in their first formal meeting since he took office.
The bombing of the pop concert in Manchester on Monday night, came a year and a half after another assault claimed by Daesh at a rock show at the Bataclan in Paris.
Maintaining pressure on Russia
Tusk called on G7 leaders to maintain sanctions on Russia over the conflict in Ukraine, but the White House said it did not yet "have a position" on the issue.
The EU and US under then president Barack Obama imposed sanctions on Moscow over its 2014 annexation of Crimea and fighting in eastern Ukraine between government forces and pro-Russia rebels.
But it is unclear whether Obama's successor Trump, who is under fire domestically over allegations that Russia meddled to aid his election campaign last year, will maintain these sanctions.
"Since our last G7 summit in Japan, we haven't seen anything that would justify a change in our sanctions policy towards Russia," Tusk, who coordinates policy for the EU's 28 leaders, told reporters in Sicily.
North Korea will "be solved"
Trump promised that North Korea "will be solved", as G7 powers will confront a series of missile tests by the nuclear-armed nation.
Trump's tough talk came in a meeting with Prime Minister Shinzo Abe of Japan, which along with South Korea is most immediately threatened by North Korean belligerence.
But the isolated regime has also threatened to target places further afield such as the US West Coast, and Trump has called North Korea's young leader Kim Jong-Un a "madman with nuclear weapons".
"We will be discussing many things including of course North Korea which is very much on our minds," Trump said before holding bilateral talks with Abe.