Washington's relations with Moscow have been particularly strained in the wake of the 2016 US presidential election, which USA intelligence agencies said was targeted by Russian Federation.
But the prime minister warned against a "tit-for-tat" response.
A senior Government source said: "The PM has always said we should engage with Russian Federation but beware".
Trump made the comment at the White House Friday after hours of further escalating his rhetoric against longtime allies over US trade practices. "I am heading for Canada and the G7 for talks that will mostly center on the long time unfair trade practiced against the United States".
Iranian President Hassan Rouhani, whose country is an observer member of the SCO, will also attend the summit at a time when China and Russian Federation are seeking to save the Iran nuclear deal following Trump's withdrawal from the pact. Under Trump, the United States has abandoned its traditional role in the G-7 as an advocate for freer global trade, instead pushing more protectionist policies.
"If there are to be any conversations about Russia's future in relation to this particular group, they have to change their ways, they have to change the route that they are taking and the sort of activity they are involved in", Mrs May said. And he emphasized a "good relationship" with French President Emmanuel Macron, saying they sometimes have a "little test" on trade, but predicting a positive outcome.
Last month, President Donald Trump pulled out of former President Barack Obama's landmark 2015 nuclear accord with Iran over the objections of European allies and other nations.
Aide Who Made Comment About McCain ‘Dying’ Out at WH
Sadler was responsible for compiling and distributing talking points to allies of the Trump administration. John McCain (R-AZ) being irrelevant because she predicted he would soon succumb to brain cancer.
The Chinese president said the three countries should push the construction of the China-Mongolia-Russia economic corridor, actively explore cooperation in areas such as infrastructure interconnectivity, and promote sub-regional cooperation in adjacent areas of the three countries.
Russian Federation joined the group in the 1990s after emerging from the wreckage of the Soviet Union, making it the G-8, but its armed intervention in its neighbor Ukraine in 2014 and seizure of the Crimean peninsula angered other major powers.
Velshi picked up on the "you're not more important to me because you're an ally" aspect of what Trump is doing on trade.
The expert also noted that during the Crimea occupation back in 2014, women and children were put in front of Russian troops as the latter started blocking Ukrainian Navy and Army bases in Crimea.
Newly sworn Italian Prime Minister Giuseppe Conte said he supports Trump's proposal.
Trudeau and his fellow G7 leaders will try to persuade Trump to reverse the duties when they meet him during the summit.
But all the leaders did endorse Mr. Trump's historic denuclearization talks with North Korean leader Kim Jong-un in Singapore next week.