Congressional Republicans on Thursday swore they weren't done trying to repeal Obamacare after President Trump signed an executive order borne out of frustration over Congress' inability to eliminate the law.

Trump signed an order Thursday aimed at loosening the healthcare law's insurance regulations and added that he will push Congress to repeal the law.

"We will also pressure Congress very strongly to finish the repeal and replace of Obamacare once and for all," he said as he signed the order.

Several congressional Republicans praised the order but took time to mention that they are still committed to replacing Obamacare.

"I will continue to push for our legislation which will return healthcare power and decision-making to patients and states," Sen. Lindsey Graham, R-S.C., said after Trump signed the order Thursday.

Graham led an overhaul bill with Sen. Bill Cassidy, R-La., that would have given Obamacare funding to states through block grants and cut Medicaid. Senate leadership shelved the bill last month after too many Republicans said they would oppose it.

Cassidy said he will "continue to work" with Trump on legislative solutions.

The House passed an Obamacare repeal bill in May, but the Senate failed to pass three Obamacare repeal bills over the summer.

Rep. Mark Meadows, R-N.C., the leader of the conservative House Freedom Caucus, said Trump's order is a step in the right direction.

"Congress would do well to follow the president's lead and renew our push to keep our seven-year promise to repeal and replace Obamacare," he said. "Failure on that end should not be an option."

The GOP's failure to pass the Graham-Cassidy overhaul bill last month put Obamacare repeal on ice for now. The GOP has pivoted to tax reform and hopes to pass a tax bill by the end of the year.

Several Republicans have said they hope to take up Obamacare repeal again after they are finished with overhauling the tax code.

The GOP can afford only two Republican defections out of its 52-48 majority, as it hopes to use a legislative tool called reconciliation to pass Obamacare repeal with only 51 votes. Vice President Mike Pence can break a 50-50 tie.

Three Republicans publicly opposed the Graham-Cassidy bill, sinking its chances. Other repeal bills failed to win 50 votes in late July, including a skinny repeal bill that was seen as a vehicle to start talks with the House.