European Commission President Jean-Claude Juncker offered to visit Washington for an assessment of EU-US trade to help resolve the dispute, an official said.
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 U.S. allies.
Under the plans agreed by the UK, US, France, Germany, Canada, Italy and Japan at the summit in Quebec, there will be greater co-ordination to identify and respond to threats including cyber attacks and other breaches of global rules.
The US has slapped a 25% tariff on imports of steel and 10% on aluminium from countries including the United Kingdom and the rest of the European Union.
Trump has invoked a United States national security provision to unilaterally impose tariffs on imports of foreign steel and aluminum, to the outrage of his allies, who have retaliated with a threat of their own, more targeted, sanctions.
G7 leaders demanded Saturday that Russian Federation stop what they described as attempts to undermine democracy and support for the Syrian regime as they closed the door on Moscow's readmission to the club.
"I think it would be an asset to have Russian Federation back in, I think it would be good for the world, I think it would be good for Russian Federation, I think it would be good for the United States, I think it would be good for all the countries of the current G7".
Asked about Trump's tariffs in March, Spain's Economy Minister Roman Escolano said that most countries at the summit shared the "belief that protectionism is a huge historical mistake".
Mr Putin spoke during a meeting ahead of a summit in Beijing featuring their two countries and six Asian states.
In an interview Sunday on German public television, Merkel also says European leaders won't be "taken advantage of" on trade. I think it would be good for all of the countries of the current G7.
"What we did this weekend, was come together, roll up our sleeves and figure out consensus language that we could all agree to on a broad range of issues".
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".
Trudeau said the G7 had agreed to an "ambitious" communique, but he acknowledged the leaders left La Malbaie without significantly transforming Trump's increasingly confrontational approach to trade. Putin added that a thorough discussion is needed to address the issue.
The US leader fired off a series of messages on Twitter hitting out at his counterparts before the summit even opened. "They should let Russian Federation come back because we should have Russian Federation at the negotiating table".
Mrs May pleaded with fellow leaders to step back from the brink of a damaging trade war at a session of the summit on Friday night.
Tweeting in English, Macron stressed: "No leader is eternal".
European leaders warned Trump's stance on trade, climate, Iran and - now - Russian Federation was setting him apart, and Canada firmly rejected the tariffs threat and threatened retaliation.
Canada, in particular, has taken offense at the notion that the steel tariffs are justified on the basis of national security concerns.
The European Commission has confirmed it intends to hit back with retaliatory tariffs from July on USA imports ranging from jeans to bourbon whiskey.
Trump's comments on agriculture, his imposition of steel and aluminum tariffs, as well as broader disagreements on trade, climate change and the USA withdrawal from the Iran nuclear agreement, are setting the stage for some tense G7 talks once Trump arrives at the summit in the Quebec town of La Malbaie.