Sen. Rand Paul, R-Ky., isn't ready to give up yet on repealing and replacing Obamacare after the House GOP pulled the American Health Care Act from a vote on Friday, despite President Trump's insisting that his administration is moving on to tax reform.

"I think legislators can walk and chew gum hopefully at the same time, so why don't we do both? Why don't we set up a special committee," Paul told Fox News fill-in host Eric Bolling on "The O'Reilly Factor" Friday evening.

Paul, who was an ally to the House Freedom Caucus in their holdout over the Obamacare replacement bill, said the Trump administration should host the group, as well as House and Senate leadership at the White House and begin a "continuing conversation" about overturning the Affordable Care Act. Trump had met with members of the HFC multiple times during the past few days in the run-up to the expected vote.

"It doesn't have to be at the breakneck pace that it has been the last three days, but let's keep talking about it until we work it out," Paul said. "If we are going to talk about taxes simultaneously and move legislatively to that before we have the answer, so be it. But you can work both tracks, and whichever one comes to a resolution first, bring it to the floor for a vote."

Paul, a physician by trade, said he still has a "great deal of optimism" that the GOP-controlled House and Senate will repeal Obamacare and can work out the replacement aspect.

"I think that President Trump's been very open too many of our ideas. I just think we didn't have enough time and we set an artificial deadline and instead of saying we're going to work until we finally get this. I don't see a reason why we can't work next week, the week after, the week after, but we should work on repealing Obamacare and I'm going to continue to be for that as well as replacing it," added Paul.

In the interim, Paul said he is urging Senate Majority Leader Mitch McConnell to take up legislation that would let people join buying groups or co-ops.

Paul added that Senate Democrats should support that policy because it would give consumers better drug and insurance prices.