President Trump should use sanctions and other policy tools to "apply pain" to Russian President Vladimir Putin over the 2016 election interference, according to a member of the Senate Intelligence Committee.

"We need to continue to apply real pressure to the Russians to say, 'You did this, so here's the consequences of that,'" Sen. James Lankford, R-Okla., said Monday during an NPR interview.

Trump raised the issue of the 2016 election cyberattacks at the outset of his first face-to-face meeting with Putin at the G-20 summit in Hamburg, Germany. Putin denied involvement in the hacks, which involved attempts to compromise state election systems and a successful effort to steal Democratic documents and leak them throughout the fall election season.

"Now it is time to move forward in working constructively with Russia!" Trump tweeted Sunday.

Lankford said that he is "pleased" Trump broached the subject in the Putin meeting, but said it doesn't amount to "real pressure" unless there is some follow-up action.

"No, real pressure is in follow-up and what you actually do in the actions afterwards," Lankford said. "A verbal back and forth, did you do it, no I didn't, is not real pressure. Real pressure is what you do with sanctions, what you do to apply pain."

Secretary of State Rex Tillerson contributed to the impression that the Trump administration doesn't plan any punitive action for the cyberattacks in his comments following the meeting. "I think the relationship — and the president made this clear as well — is too important," Tillerson told reporters Friday. "And it's too important to not find a way to move forward."

Trump and Putin "agreed to explore creating a framework" for cybersecurity. "It needs to be addressed in terms of how we assure the American people that interference in our elections will not occur by Russia or anyone else," Tillerson told reporters at an ensuing Sunday press conference.

Lankford was part of a veto-proof majority of senators who voted to impose a broad package of sanctions on Russia, related to the elections as well as Putin's policies in Syria and Ukraine. Tillerson wants House lawmakers to change the bill so that Trump will have more discretion over whether to impose or relax the sanctions.

"I would urge Congress to ensure any legislation allows the president to have the flexibility to adjust sanctions to meet the needs of what is always an evolving diplomatic situation," Tillerson told lawmakers in June.