Speaking to reporters Thursday afternoon, Trump declined to say whether McConnell should resign but said they should ask the question again if the Senate leader doesn't deliver on the president's leading priorities.
Declaring that he was "very disappointed in Mitch," Trump said he was particularly miffed by a Senate vote to repeal the Affordable Care Act that failed by a single vote.
"For a thing like that to happen is a disgrace, and frankly it shouldn't have happened," he said.
Trump associates said the attacks, which began Wednesday night and resumed Thursday, were intended to shore up Trump's outside-the-Beltway populist credentials and would resonate with core supporters frustrated by a lack of progress in Washington.
But the tweets were quickly met with public and private defenses of McConnell — and rebukes of Trump.
Sen. Orrin G. Hatch (R-Utah), tweeted: "@SenateMajLdr has been the best leader we've had in my time in the Senate, through very tough challenges. I fully support him."
Scenes from Trump’s second six months in office
Former House speaker Newt Gingrich (Ga.), a Trump adviser, said on Fox News Channel that the president bears some responsibility for the Republican failure on the health-care legislation.
"I think the president can't dissociate himself from this," Gingrich said. Trump "is part of the leadership team. He is not an observer sitting up in the stands. He is on the field. It was a collective failure."
Even some Republicans close to the president suggested that the attacks on McConnell would hurt him on Capitol Hill, where relations with GOP leaders have seriously frayed as Trump's agenda has stalled.
"Yelling at his Senate quarterback isn't going to help him achieve these wins," said one GOP strategist close to the White House who spoke on the condition of anonymity to be candid.
Trump, who is on a working vacation at his private golf club in Bedminster, N.J., remains bitter about the collapse of Republican efforts to repeal and replace former president Barack Obama's health-care law, a pledge the party has made since 2010 and a marquee campaign promise for Trump.
"Can you believe that Mitch McConnell, who has screamed Repeal & Replace for 7 years, couldn't get it done," Trump wrote on Twitter on Thursday. "Must Repeal & Replace ObamaCare!"
A few hours later, the president took to Twitter again, writing: "Mitch, get back to work and put Repeal & Replace, Tax Reform & Cuts and a great Infrastructure Bill on my desk for signing. You can do it!"
The tweets came in the wake of McConnell's suggestion earlier in the week that Trump's lack of political experience had led to "excessive expectations" for passing major legislation.
The president has faced heavy criticism for the fate of the health-care legislation. While he repeatedly called on lawmakers to dismantle the Affordable Care Act, he did relatively little to help develop — or sell — their replacement plans to the public at a time when polls showed the effort was highly unpopular.
Trump's attacks this week come as lawmakers are poised to try to tackle other shared but challenging priorities when they return from their August recess. Besides Trump's leading agenda items, they also are faced with trying to craft a budget and raise the nation's debt ceiling.
"Discerning a particular strategy or goal from these tweets is hard," said Doug Heye, a former Republican National Committee communications director and a former Capitol Hill staff member. "It just doesn't help enact any part of his agenda, and it sends a further troubling sign to Capitol Hill Republicans already wary of the White House."
Heye said that with Trump's job-approval numbers declining among the Republican base, "now is the time to build support within the party."
White House aides said Trump has a general frustration with McConnell that extends beyond the health-care debate.
"You can see the president's tweets," White House press secretary Sarah Huckabee Sanders told reporters Thursday. "Obviously, there's some frustration."
McConnell has been one of the most steadfast supporters of Trump's agenda in Congress, and, at least publicly, Trump has had a smoother relationship with McConnell than he has with House Speaker Paul D. Ryan (R-Wis.) and other congressional leaders.
In April, McConnell orchestrated the confirmation of Neil M. Gorsuch, Trump's Supreme Court pick, changing the Senate rules so that Democrats could not block the nomination. The Gorsuch confirmation is Trump's largest victory on Capitol Hill.
McConnell's wife, Elaine Chao, another prominent Washington figure, serves in Trump's Cabinet as transportation secretary. Trump said Thursday that Chao "is doing a very good job."
In his remarks Monday to the Rotary Club in Florence, Ky., McConnell said, "Our new president had, of course, not been in this line of work before." He added, "I think he had excessive expectations about how quickly things happen in the democratic process."
Sanders said that Trump and McConnell spoke by phone Wednesday, a conversation in which Trump made clear that he wants to continue to press for passage of a health-care bill. The same day, Trump took his first shot at McConnell on Twitter.
"Senator Mitch McConnell said I had 'excessive expectations,' but I don't think so," the president wrote. "After 7 years of hearing Repeal & Replace, why not done?"
In another sign of frayed relations between Trump and Republican senators, one of the president's largest political benefactors is providing a $300,000 contribution to a super PAC that aims to unseat Sen. Jeff Flake (R-Ariz), who has been critical of Trump.
Politico first reported that Robert Mercer, a hedge-fund billionaire heavily involved in Trump's political ascendancy, is making a donation to a group supporting former Arizona state senator Kelli Ward, who is challenging Flake in a Republican primary next year.
Ward emailed a fundraising pitch to supporters Thursday, calling out McConnell for "finger-pointing at President Trump" instead of working to pass a GOP health-care plan.
Flake, meanwhile, defended McConnell, saying that the leader "has a tough job and I think he does it well."
Despite the public criticism, Trump and McConnell have been in frequent contact, usually by telephone, to discuss legislative strategy, aides said.
Privately, senior GOP congressional aides across Capitol Hill have said it's Trump and his team — not McConnell — who deserve the blame for the collapse of the GOP's health-care plan. The aides gripe that Trump seriously damaged relationships with key Republican senators over the months-long debacle.
At one point this summer, Trump was flanked at a White House meeting by Sens. Susan Collins (R-Maine) and Lisa Murkowski (R-Alaska), who both voted against the health-care measure. At the mid-July meeting, it was Sen. Dean Heller (R-Nev.) seated next to Trump. The president called him out with cameras rolling for wavering on the health-care bill.
"Look, he wants to remain a senator, doesn't he?" Trump said as Heller laughed uncomfortably.
Heller ultimately voted for the bill, but the exchange with Trump is a scene that Democratic aides have vowed will appear prominently in future campaign attack ads against the senator, who is the most vulnerable Republican facing reelection next year.
Trump's long-standing feud with Sen. John McCain (R-Ariz.) hasn't helped the overall dynamic either. The senator voted against the health-care plan in a closely watched late-night vote — even after Trump made a direct last-minute appeal by phone.
O'Keefe reported from Prescott, Ariz. Philip Rucker in Bedminster, N.J., and Kelsey Snell in Washington contributed to this report.