The Trump administration has prepared an executive order that would unravel Obamacare's individual mandate, but has put it on hold to see whether repealing the penalties for going uninsured might be included in the Republican tax bill instead, a GOP senator told the Washington Examiner.

President Trump decided to delay the executive order after Sen. Tom Cotton, R-Ark., pushed for the inclusion of the individual mandate repeal in the tax bill, and has been supportive of its inclusion in statements he has made on Twitter.

After initially declining to comment on the senator's statements, a White House official pushed back on the claims, saying the administration's position is that Congress should resolve the issue.

"Pursuant to the President’s January EO on Obamacare, we are always looking for ways to provide relief from Obamacare," the White House official said. "The long-standing issues with the mandate would be best resolved legislatively."

The senator had told the Washington Examiner that an executive order was sitting with the Office of Management and Budget waiting for approval, but an official from the agency denied it.

"There is no EO on the individual mandate at OMB," the official said.

Asked about the comments, the senator stood by the assertion that the executive order was ready, and said the administration might be being vague in its responses to maintain negotiating flexibility.

Including repeal of the individual mandate's penalties in the tax bill instead of through executive order would create billions in budget savings that Republicans need to pay for tax cuts. According to a Congressional Budget Office report published in December 2016, repeal of the individual mandate would save $416 billion over a decade, since it would mean fewer people would be enrolled in Medicaid and fewer subsidy payments would go to people who sign up for private coverage. A new CBO report is expected Monday.

Repeal is not currently in the tax bill, known as the Tax Cuts and Jobs Act, but House Speaker Paul Ryan said this weekend that it was on the negotiation table among House Republicans.

"We have an active conversation with our members on a whole host of ideas on things to add to this bill and that's one of the things being discussed," he said.

The senator who spoke to the Washington Examiner, who asked to remain anonymous, thinks colleagues could embrace repeal in the tax bill, because the revenue generated "pays for so many tax cuts."

The individual mandate is among the most unpopular portions of Obamacare, as it obligates people to purchase health insurance or pay a fine. Proponents argue that some impetus is needed to bring healthier, younger customers into the Obamacare exchanges to balance out the medical claims of more expensive customers. Critics say that it has been ineffective in doing so, noting that CBO projected 24 million people would sign up for Obamacare plans but that the number after the last open enrollment fell closer to 13 million.

Though Republicans have said they are committed to repealing the individual mandate, some have said that they are concerned its inclusion in the tax bill would cause the legislation to hit a snag.

Its effects would be similar to the "skinny repeal" bill that Republicans failed to pass this summer after three GOP senators opposed it. The CBO report on the bill projected the repeal of the individual mandate would result in 15 million more people becoming uninsured.

Trump cannot repeal the individual mandate through executive order, but he can direct the secretary of the Department of Health and Human Services to broaden "hardship exemptions," which under Obamacare are left to the discretion of the administration. The exemptions allow customers to have ways to get out of paying the fine for not having coverage, which is $695 per adult or 2.5 percent of income, whichever is higher.

The Obama administration created hardship exemptions for a range of situations, including if someone filed for bankruptcy, experienced a flood, death of a family member, domestic violence or a shut-off notice from a utility company.

The majority of Americans have health insurance coverage through work or through a government program and meet the individual mandate requirement. Customers who buy coverage under Obamacare, whether on the exchange or directly through an insurer, are most directly impacted by the individual mandate.

About 6.5 million taxpayers paid penalties for failing to have coverage in 2015, according to the IRS. Data from the Kaiser Family Foundation show that 28 million Americans are uninsured.

Trump's executive order alternatively could essentially make it against the administration's policy to collect fines from people who don't have health insurance coverage, the Republican senator said.

David M. Drucker and Gabby Morrongiello contributed to this report.

This story has been updated with additional information, including statements from White House and Office of Management and Budget officials.