However, Trump did seek to lower the temperature after his arrival.
At stake is the risk of tit-for-tat tariffs between the major western economies turning into an unrestrained trade war.
Still, the fundamental differences remained clear.
He added, however, that no concrete agreements have been reached and no concrete discussions were underway.
The Wall Street Journal reported early in June that the White House was preparing for a potential summit between the two leaders, which a senior administration official called an "ongoing project" of Jon Hunstman, the USA ambassador to Russian Federation.
"Let's remember why the G8 became the G7".More news: Donald Trump says Russian Federation should be be allowed to rejoin G7
Russian Federation was removed from the summit in 2014 after its forced annexation of Crimea away from Ukraine. In a joint statement, then-President Barack Obama and other world leaders condemned Russia's actions as "violat [ing] the principles upon which the worldwide system is built".
The agreement is based on greater intelligence sharing between the countries of the G7 group of industrialised nations - Canada, France, Germany, Italy, Japan, UK and the USA - and aims to identify, prevent and respond to hostile state activity including cyber-attacks.
European Union President Donald Tusk, who was also attending summit, also rejected Trump's suggestion. He's punishing our allies, he's not showing them very much respect, showing up at this meeting late.
The summit has already been dubbed the "G6 plus one" due to Mr Trump's isolation over trade and his decision to pull the United States out of the Iran nuclear deal.
"Looking forward to straightening out unfair Trade Deals with the G-7 countries".
Relations have hit such a low point that a key question now is whether the seven countries can agree on a joint statement of priorities at the conclusion of the meeting.More news: Crude Down as Saudis Said to be Revisiting Oil Cut Policy
Trump has repeatedly put himself at odds with practically the entire United States political and security establishment over Russian meddling in the 2016 Presidential Election.
Ahead of the annual meeting of G7 leaders Trump said Russian Federation should be allowed back, a suggestion quickly rejected by Britain, France and Germany. "But there's one circumstance that I've mentioned previously: Trump keeps the promises that he made in his campaign".
The French president did have some private time with Trump before the summit officially started. "Russian Federation should be in this meeting".
The Russian leader knows that America's global power rests not only on our military and economic might but also on our unrivaled network of alliances from Europe to Asia.
Xi and Putin also vowed to make "all possible efforts" to preserve the 2015 worldwide accord on Iran's nuclear programme that Trump abandoned last month.
At the G7, only Italy's new populist Prime Minister Giuseppe Conte said he agreed that Moscow should be back in the fold.More news: Live coverage of big reveals including Federation Internationale de Football Association 19
Putin said last month that the proposed summit between him and Trump was not working out for now and was beset by problems. "In the interest of all".