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Story highlights

McConnell has been an outspoken critic of Trump's over the past several days

He would not rescind his endorsement of Trump

(CNN) —  

Senate Majority Leader Mitch McConnell said Wednesday Donald Trump’s toned-down, teleprompter-read primary night speech was a “good start” but he still has plenty of work to do to satisfy his party’s leadership.

The Kentucky Republican has been an outspoken critic of Trump’s over the past several days, calling comments he made about an Indiana-born federal judge’s Mexican heritage “totally inappropriate.”

But McConnell told CNN”s Erin Burnett on “OutFront” he saw a glimmer of hope on primary night.

“Using a prepared text last night and not attacking any other Americans was a good start,” McConnell said.

But – he added – there’s still plenty of room for improvement.

“I think it’s still time for him to act like a presidential candidate should be acting,” McConnell said. “So I haven’t given up hope, but certainly last week was not a good week for Donald Trump.”

RELATED: Gingrich: Trump a ‘gifted amateur’

McConnnell called the speech a “good step in the right direction.”

Recalling an anecdote from when his meeting last month with Trump at the National Rifle Association convention, McConnell said he pitched being “boring” to the businessman.

“I said, ‘Hey Donald, have you got a script?’” McConnell told Burnett. “He pulled out his pockets and said, ‘I hate a script, it’s so boring.’ I said, ‘Put me down in favor of boring.’ “

Though Trump was muted Tuesday night, he has stood by calling U.S. District Court Judge Gonzalo Curiel a “hater” and “a Mexican,” telling Fox News on Tuesday that Republicans who have critiqued him need to “get over it.”

McConnell said that Trump doesn’t “yet” seem to be fully on board with what the party is asking him to do, but still held out hope that he could turn it around.

“Donald Trump’s got a lot of good qualities but he’s got to put them forward and suppress some of these other actions,” he said. “He needs to begin to act like a presidential candidate.”

And McConnell said even if Trump doesn’t, he would not rescind his endorsement of Trump and was backing him as the party’s standard-bearer.

“He’s been chosen by the Republican primary voters across the country,” McConnell said. “He’s going to be the nominee. What most of us would like to see is him run a campaign that gives him a chance of victory.”