Senators should make progress on health-care legislation before leaving Washington for their August recess, President Donald Trump said on Wednesday.

"We have to stay here. We shouldn't leave town, and we should hammer this out and get it done," Trump said.

GOP senators planned to work late into the night to try to find a way to revive the effort to repeal and/or replace Obamacare, according to an Axios report.

The president's comments come after a Republican proposal to simply repeal Obamacare quickly lost support among GOP senators. That proposal came after the most recent draft of a replacement bill collapsed on Monday after four Republicans said they opposed it.

On Tuesday, the president said he was "disappointed" with the failure. At the time, Trump repeated his belief that it would be easier to simply let President Barack Obama's signature health-care law fail on its own.

But the president on Wednesday called for renewed efforts to draft health-care legislation, instead of letting Obamacare implode. While a repeal would be "fine," the president said, Republicans should try to "get more."

"I think the people of this country need more than a repeal. They need a repeal and a replace, and we were very, very close," Trump said.

"We have no choice. We have to repeal and replace Obamacare. We can repeal it, but the best is repeal and replace. And let's get going. I intend to keep my promise, and I know you will, too."

Following the president's comments, Senate Majority Leader Mitch McConnell told reporters after the lunch that the Senate would proceed next week with a vote on a motion to move ahead with a repeal bill. The proposal does not include a replacement plan, though it could be amended, he said.

"I think we have two options here. I think we all agree it's better to both repeal and replace, but we could have a vote on either, and if we end up voting on repeal only, it will be fully amendable on the Senate floor," McConnell said. "And if it were to pass without any amendment at all there's a two-year delay before it kicks in ... so the takeaway from what I'm telling you is no harm is done from getting on the bill."

Republicans have campaigned on repealing Obamacare since it was enacted. But the GOP effort to strike down the law has been stymied by divisions within the party. Delays in health-care reform push back the rest of the Republican agenda, which includes tax reform.

The president said that senators who vote against starting debate on a health-care bill would be telling Americans they're fine with Obamacare.

"But being fine with Obamacare isn't an option for another reason because it's gone. It's failed. It's not going to be around," he said.

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Not dead, yet: Trump pushes GOP senators to repeal Obamacare - CNBC