The Kremlin has denied that the Russian government interfered in the USA election.
According to White House press secretary Sarah Sanders, however, the summit is "still on" despite calls that it be cancelled.
But other Republican lawmakers expressed the same sentiment as House Foreign Affairs Chairman Ed Royce of California, who said in a statement that Trump should "should use today's indictments to challenge" Putin at the meeting.
MacCallum brought up the indictments of the 12 Russian intel officers on hacking charges, and Graham restated, "I want President Trump to go to meet Putin, I want a better relationship, but when Putin says 'I didn't do it, ' I want President Trump to say, 'I reject that denial".
Twelve Russian intelligence officers were indicted on charges they hacked into Democratic email accounts during the 2016 US presidential election and released stolen information in the months before Americans headed to the polls, the Justice Department said Friday.
The White House didn't respond to a request for further comment on whether Trump would address the indictments when he meets with Putin.
The charges come as special counsel Robert Mueller investigates potential coordination between Russian Federation and the Trump campaign to influence the presidential election. "We'll be talking to President Putin about a number of things: Ukraine. We should stand united against Putin's past and planned future attacks against us".
Lawmakers on both sides of the aisle Friday called on President Donald Trump to consider canceling his upcoming summit with Russian President Vladimir Putin in Finland after new indictments in the special counsel probe headed by Robert Mueller.
Rosenstein said the president had been briefed on the charges earlier this week.
'I think that really hurts our country and it really hurts our relations with Russia, ' Trump said. Referring to a TV courtroom drama aired in the 1950s and 1960s that often featured a dramatic, last-minute confession, he added, "There won't be a Perry Mason here, I don't think, but you never know what happens, right?"
Intelligence agencies have said the interference was aimed at helping Trump's presidential campaign and harming the election bid of his Democratic opponent, Hillary Clinton.
But just hours before Rosenstein's announcement, the president continued to say the investigation was a "witch hunt" and hurt the relationship between the US and Russian Federation.