(CNN) Republican senators criticized President Donald Trump on Wednesday for congratulating Russian President Vladimir Putin on winning another term and not calling him out on Russian meddling during the 2016 presidential election.

"I haven't heard anybody in the legislative branch say they think it's a great idea," said Sen. John Cornyn, the No. 2 Republican in the Senate.

Asked for his own opinion of the call, Cornyn stressed, "I don't think it's a great idea."

Republican Sen. Marco Rubio of Florida disapproved of Trump making the call, but he said he was more disappointed by leaks from the White House that revealed Trump's national security advisers urged the President not to congratulate Putin before the call.

"So, I don't like what he did, but I really hate that there's someone in his inner circle that's willing to leak this stuff," Rubio said. "If you don't like working for the President, you should resign your job."

Republican Sen. John Kennedy of Louisiana downplayed the Putin call as "polite" and blasted White House staff for the leak, saying whoever is responsible should be prosecuted and added that if he were king for a day, he would "hit (Putin) so hard with sanctions that he would cough up bones."

Putin has won his position for another six years after his sweeping victory in Russia's election on Sunday , a result that was expected. He was already the country's longest-serving leader since Soviet dictator Joseph Stalin.

Sen. Chuck Grassley, chairman of the Senate Judiciary Committee, declined to share his opinion on Trump making the call, but he said personally "wouldn't have a conversation with a criminal" and didn't hold back when talking about his heavy dislike of the Russian leader.

"I think Putin's a criminal," he said. "What he did in Georgia, what he did in Ukraine, what he's done in the Baltics, what he's done in London -- poisoning people with nerve gas, that's a criminal activity."

Their comments followed Senate Majority Leader Mitch McConnell remark Tuesday such a call would not have been "high on my list."

"The President can call whomever he chooses," McConnell said at a news conference. "When I look at a Russian election, what I see is a lack of credibility in tallying the results I'm always reminded of the elections they have in almost every communist country, where whoever the dictator was of the moment, always got a huge percentage of the vote. So, calling him wouldn't have been high on my list."

The Trump administration last week announced it was enacting new sanctions on Russia , several months after Congress mandated that punitive measures against Russia for its cyber attacks against the United States.

White House press secretary Sarah Sanders defended the President on Tuesday for the phone call, saying "we disagree with the fact that we shouldn't have conversations with Russia."

"There are important topics that we should be able to discuss," she told reporters in the press briefing.

Sanders later declined to say whether Russia's election was "free" and "fair."

"We don't get to dictate how other countries operate," she added. "Putin has been elected in their country and it not something we can dictate to them how they operate."

Her response was in reaction to Republican Sen. John McCain, who strongly condemned the call in a statement on Tuesday, saying an American president shouldn't congratulate "dictators on winning sham elections."

"President Trump insulted every Russian citizen who was denied the right to vote in a free and fair election to determine their country's future, including the countless Russian patriots who have risked so much to protest and resist Putin's regime," he said.

Some Republicans, however, said they had no problem with Trump making the call. Sen. Bob Corker, chairman of the Foreign Relations Committee, said he personally didn't consider the Russian contest a real election but he said it's "fairly normal" to congratulate another country's leader.

"Especially when you've ... got major nuclear treaties between us and that kind of thing," Corker said Tuesday. "I think it's, you know, fine. I don't read anything into it. I don't see anything wrong with it."

This story has been updated and will continue to update with additional developments.