By Ted Barrett and Manu Raju, CNN

(CNN) -- Senate Majority Leader Mitch McConnell forcefully defended Robert Mueller on Tuesday, saying the special counsel should be allowed to finish his investigation and that legislation was "not necessary" to protect him against the threat of being fired by President Donald Trump.

McConnell also was critical of Trump's decision to call Russian President Vladimir Putin to congratulate him on his recent election victory.

"I agree with the President's lawyers that Bob Mueller ought to be allowed to finish his job. I think he was an excellent appointment," McConnell told reporters at his weekly news conference in the Capitol. "I think he will go wherever the facts lead him and I think he will have great credibility with the American people when he reaches the conclusion of his investigation. So, I have a lot of confidence in him."

It was McConnell's first public comments since January about Mueller and the possible need to pass legislation to preserve his job -- a debate that has been swirling in public for weeks.

Asked if legislation should be passed to protect Mueller, whom Trump has repeatedly blasted on Twitter, the Kentucky Republican said, "I don't think that's necessary. I don't think Bob Mueller is going anywhere. I think there is widespread feeling, and the President's lawyers obviously agree, that he ought to be allowed to finish the job."

"He is a thoroughly credible individual," McConnell added, heaping even more praise on Mueller.

Senate Minority Leader Chuck Schumer praised McConnell's defense of Mueller — calling it a "shot across the bow."

"I want to salute his statesmanship," the New York Democrat told reporters of McConnell's statement. "That was the right thing to do. And I certainly hope President Trump is listening."

McConnell did not answer a question as he walked away from the microphones about what actions he would take if Trump did fire Mueller.

On Trump's call with Putin, which was slammed in a statement by Arizona GOP Sen. John McCain, calling Putin a "dictator" who won a "sham election," McConnell said such a call would not have been "high on my list."

"The President can call whomever he chooses," McConnell said. "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."