Mr Putin, speaking during a visit to China, said: "We did not choose to leave it, our colleagues refused to come to Russian Federation due to known reasons at some point".
"We should remind ourselves why the G8 became the G7, it was because Russian Federation illegally annexed Crimea".
Putin has been driven closer to China by a sharp decline in relations with the West after Moscow's 2014 annexation of Crimea and support for a separatist insurgency in eastern Ukraine.
Trump attended the 44th G7 summit which kicked off in Charlevoir, Canada on Friday.
The EU members of the G7 had a special meeting in the margins of the summit to discuss tariffs and the Iran nuclear deal, which Mr Trump also opposes.
But what has changed since Russia's ouster is Trump's election.
"Our relationship is very good", Trump said.
The U.S. president had also slammed America's Western trading partners, saying "all of these countries have been taking advantage of the United States on trade".
That comment has Trump squarely offside with this fellow G7 leaders, including Canada, who view Russia's annexation of Ukraine's Crimean Peninsula and its meddling in western elections as a major worldwide security concern. He added: "We have to straighten it out".
Merkel and Trump also had a brief conversation at the summit but no bilateral meeting.
"Let's leave seven as it is", Tusk said.
The White House has downplayed reports of tensions between the leaders, but stressed that the president is committed to overhauling trade practices.
Mnuchin said Russia's "malign" activities included cyber intrusion into the US energy grid and other infrastructure; an internet-chewing worm called Notpetya that cost several global conglomerates millions of dollars in damages; and the tracking of and possible interference with undersea communications cables that carry most of the world's telecommunications data.
Canada's foreign minister Chrystia Freeland expressed outrage that Trump had invoked a national security justification for his global tariffs, even on imports from close United States allies.
Trump arrived late for Saturday's meeting during the Group of Seven summit of leading industrialized nations being held in Quebec.
Trump angered his G7 allies last week by slapping them with hefty tariffs on steel and aluminum - a move that prompted Canada and the European Union to threaten duties of their own. "And if it's not fixed, then we're not going to deal with these countries".
Germany's Angela Merkel says nothing has changed when it comes to Russian Federation. "Please, we would be happy to see everyone in Moscow".
"No matter what fluctuations there are in the global situation, China and Russian Federation have always firmly taken the development of relations as a priority", Xi told Putin.
Referring to the Mueller investigation, and the possibility it may result in criminal charges against him, Trump maintained he has "the absolute right to pardon myself", adding "but I'll never have to do it because I didn't do anything wrong". "Economic globalization and regional economic integration are the trend of the times", Xi said.
"The rules-based global order is being challenged, not by the usual suspects but by its main architect and guarantor: the United States", said European Council President Donald Tusk. Ali was convicted in 1967 of avoiding military service.
Trump said he had a list of 3,000 names for possible pardon consideration. From there, he planned to jet to Singapore for an unprecedented summit with the leader of North Korea, which is technically still in a state of war with the USA and considered by Trump's administration to be a state sponsor of terrorism.