"The case is closed," he said.
"They want him to read his report? The American people have moved on from this. You saw the vote over in the House recently on taking up impeachment. It didn't get much support. I think they don't understand that presidential harassment all the way to the election is not going to help them win."
In regard to House Democrats' hopes their agenda will be considered in the Republican-led Senate, McConnell said they will be left waiting.
"The Green New Deal would take away your job. Medicare-for-All would take away 180 million Americans' private health insurance, and if they made any effort to pay for it, they'd have to have such a massive tax increase, it would slow the economy further," he said.
"I've said as long as I'm the majority leader of the Senate, I've smilingly said I'm going to be the Grim Reaper.
"None of that stuff is going to pass the Senate. We're not going to stand by and let America become a socialist country. "
The Kentucky lawmaker, who is up for reelection for a seventh term in 2020, added, "I’m happy to go to the American people next year and have a debate about that."
With the presidential election in sight, McConnell pledged to continue holding confirmation hearings for district and circuit court judges.
"And if the American people give the president another term and we have the Senate we're going to keep on doing it," he said.