The Trump administration is aiming to complete the biggest overhaul of the tax code since President Ronald Reagan by end of the year, even if a second attempt to repeal the Affordable Care Act fails, according to Treasury Secretary Steven Mnuchin.

"Whether health care gets done or doesn't get done, we're going to get tax reform done," Mnuchin said Thursday at a conference in Washington. "We're pretty close to being able to bring forward what is going to be major tax reform."

The dollar and U.S. stocks rose after Mnuchin's comments, which come as the White House and congressional Republicans are at odds over whether to try for another vote on replacing Obamacare next week. President Donald Trump has said he wants to get a health-care bill completed first before moving onto taxes.

The White House is working on hashing out its own proposal, while the tax-writing House Ways and Means Committee is working on getting support for the tax blueprint it released in June. Both sides broadly agree on rate cuts for individuals and businesses. The Trump administration hasn't yet said whether it supports the House's controversial border adjustment proposal to replace the 35 percent corporate rate with a 20 percent tax on domestic goods and imports, while exempting exports.

"There are certain things we like" about the border-adjusted tax, but "there are certain things we don't," Mnuchin said. He cited concern over currency adjustments that underpin the proposal. Proponents of the tax say the U.S. dollar would rise 25 percent to offset the higher price of imported goods.

"If the currency does correct in a much stronger currency, then that hurts our exports, if the currency doesn't correct we have price appreciation and inflation particularly in consumer goods, then that's a concern," he said. "We're working with the House and having discussions on the specifics of it."

Mnuchin said the administration's tax priorities are to simplify personal taxes, create middle-class tax cuts and make business taxes competitive. He also said the White House's tax overhaul plan wouldn't increase the federal deficit.

"Some of the lowering of rates is going to be offset" by fewer deductions and 'simpler' taxes, he said. "But the majority will fundamentally come from growth and dynamic scoring." Dynamic scoring refers to complex economic models that take into account the impact of tax policies on economic growth and consumer well-being.

Both Trump's campaign plan and the House Republican proposal would collapse the existing seven existing income tax brackets into three, with a top rate of 33 percent. Mnuchin said Thursday that administration officials are looking at whether there should be four brackets instead of three.