The group also raised the controversial Russian hacking activities during the 2016 election.
"We must recognize and counter the active cyber and information warfare Russia is conducting, including attempted interference in our democratic elections process (with a) firm response," the letter said.
They further warned that the US "should not enter into any military or diplomatic agreement with Russia regarding Syria's future" until the Russian military ceases human rights abuses.
The group of seven Republican senators featured Sen. Cory Gardner of Colorado, Sen. Jim Inhofe of Oklahoma, Sen. Todd Young of Indiana, Sen. Rob Portman of Ohio, Sen. Mike Rounds of South Dakota, Sen. Joni Ernst Iowa, Sen. Lindsey Graham of South Carolina and Sen. John Cornyn of Texas, a senior member of the GOP senate leadership.
Gardner told CNN's "New Day" on Thursday: "It's important that we highlight the beliefs of many senators, our colleagues, across the national security committees -- that we do have certain lines that cannot be crossed when it comes to Russia."
"We're sending a letter to the president saying look, this is where we have to stand on Russia," Gardner said. "What they are doing in Ukraine is illegal and we can't lift sanctions on Russia until they stop their aggression and return Crimea. They've murdered 10,000 ... killed 10,000 Ukrainians. It's unacceptable. What they have done in Aleppo, what they have done in Syria, is unacceptable. Their activities on cyber around the globe are unacceptable, including in the United States this past year."
He added: "There is no quid pro quo there that can be given to Russian when it comes to, 'Hey, if you behave well over here, we can lift sanctions over here.' "
The group's letter reflects unease among the foreign-policy and hawkish wings of the Republican Party, who have shared concerns over Trump's close embrace of Russian President Vladimir Putin and his express desire to craft a more collaborative relationship between the two countries.
Those concerns were amplified when, in an interview on Sunday with Fox News' Bill O'Reilly
, Trump responded to questions about Russian human rights abuses: "You think our country is so innocent?"
Those opposed to Trump's Russian detente argue that the values and interests of the US and Russia are incompatible in some areas, such as the conflicts in Syria and Ukraine, and that improved relations shouldn't come at their expense.
In the letter, the senators write that "while we should seek common ground with Russian in the areas of mutual interest, we must never pursue cooperation with Russia at the expense of our fundamental interests of defending our allies and promoting our values."
The senators also called out Russian attempts to interfere in the 2016 U.S. presidential election -- a sensitive subject for Republicans, who have toed the line of acknowledging the Russian attempts to benefit Trump, while maintaining they had no effect on the outcome.
"The United States must have a firm response to this belligerent behavior from Moscow, which should include diplomatic actions, economic consequences, as well as a strengthened military posture in Europe," they said.
The group closed the letter urging Trump "to relay to Moscow that the values of democracy, human rights, transparency, and accountability are central to US foreign policy," and that "these values are non-negotiable."
The letter follows another high-profile move by Republicans in Congress seeking to take a firmer line against Russian aggression in Eastern Europe. On Wednesday, a group led by Graham and Democratic Sen. Ben Cardin introduced legislation
that would impose strict new congressional oversight and veto power over the Trump administration if it decided to lift sanctions on Russia.
The Russia Review Act would require the White House to submit a report detailing why it was seeking to lift sanctions, setting into motion a 120-day review period where Congress could vote to disapprove of easing the penalties on the country, according to a summary of the measure provided to CNN.
Sen. Marco Rubio, a member of the Senate Foreign Relations Committee, is cosponsoring the Graham-Cardin measure, along with Democratic Sens. Claire McCaskill of Missouri, Sherrod Brown of Ohio and Republican John McCain of Arizona.