Senators said Trump "should maintain the current U.S. sanctions regime" until Russian policy in Ukraine and Syria is changed.
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.
"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," Gardner told CNN on Thursday.
The letter comes after a group of U.S. senators introduced legislation that would make it harder for President Donald Trump to lift sanctions imposed on Russia for its actions in Ukraine if he seeks to do so.
The bipartisan bill was introduced on Feb. 8 amid mounting concerns in Congress about the Trump administration's policy intentions toward Russia.