Vladimir Putin and Donald Trump. Reuters/Alexander Zemlianichenko, AP Photo/Evan Vucci, Business Insider/Skye Gould Republican lawmakers say they are determined to find out what role Russia may have played in the 2016 US elections.

Despite the Republican Party's huge wins across the board — including President-elect Donald Trump's upset victory against Democrat Hillary Clinton — some in the GOP say a full accounting of Russia's alleged involvement is needed.

Senators John McCain of Arizona and Lindsay Graham of South Carolina are among the leading voices in that effort.

"See, the problem with hacking is that if they’re able to disrupt elections, then it’s a national security issue, obviously," McCain told The Washington Post in an interview on Russia's possible involvement.

Graham said of Russia, "They'll keep doing more here until they pay a price." The Post said Graham plans to hold investigative hearings next year on Russia's global "misadventures."

Graham took a more direct tone in an interview on CNN Wednesday: "I'm going after Russia in every way you can go after Russia. I think they're one of the most destabilizing influences on the world stage."

Trump, who raised eyebrows during his campaign when he appeared to show deference to Russian President Vladimir Putin, has expressed some reticence about investigating Russia. Vice President-elect Mike Pence, however, said Russia should face "severe consequences" if it was indeed meddling in the US election.

While the FBI has said there was no direct connection between Trump and Russia, the US Department of Homeland Security officially accused Russia in October of hacking the Democratic Party, citing multiple breaches that damaged party organizations and leaders.

A string of hacked documents and emails from WikiLeaks targeted Democrats and allies of Hillary Clinton almost exclusively in the months leading up to the November election.