(Adds Trump remarks, details)
WASHINGTON, Dec 13 (Reuters) - Congressional Republicans have reached a deal on final tax legislation, the top Senate Republican tax writer said on Wednesday, with President Donald Trump saying minutes later he would back a corporate tax rate of 21 percent.
That would be slightly above a proposed 20-percent rate that Trump supported earlier, but still far below the present headline rate of 35 percent, a deep tax cut that U.S. corporations have been seeking for years.
Although the president said a "final number" on the corporate rate had not been set, the Senate and House of Representatives were hurtling toward an agreement on that aspect of their legislation, and many other aspects, that would clear the way for final votes in both chambers next week.
"I think we've got a pretty good deal," Senate Finance Committee Chairman Orrin Hatch told reporters as he prepared to join other Republicans for lunch with Trump.
Asked at the lunch by reporters if he would sign a bill with a 21-percent corporate rate, Trump said: "I would ...
"We haven't set that final figure yet, but certainly 21 is ... a very great difference," he said. "It's very important for the country to get a vote next week."
The emerging congressional agreement includes a 21-percent corporate rate, a top individual income tax rate of 37 percent, down from the current 39.6 percent level, and a $10,000 cap on deducting state and local property or income tax payments, said sources familiar with the negotiations.
With their defeat on Tuesday in an Alabama special Senate election, Republicans were under increased pressure to complete their tax overhaul before Christmas and before a new Democratic Alabama senator is seated.
Hatch's remarks appeared to reinforce expectations that a final vote could begin in the Senate as early as Monday.
Democrat Doug Jones' capture of the Alabama Senate seat came hours ahead of a planned Senate-House conference meeting capping days of closed-door discussions on final legislation.
When Jones, who upset Republican Roy Moore in the deeply conservative Southern state, arrives in Washington, the Republicans' already slim Senate majority will narrow to 51-49, further complicating Trump's legislative agenda.
Fast action by Republicans on taxes would prevent Jones from upsetting the expected vote tallies on this bill since he will not likely be seated until late December or early January.
Senate Democratic Leader Chuck Schumer called on Republicans to delay a vote on overhauling the tax code for the first time in 30 years until Jones can be seated, but that was unlikely.
Before Hatch spoke, Republicans were trying to finalize details without increasing the legislation's deficit impact. It is expected to add as much as $1.5 trillion to the $20-trillion national debt over the next decade.
A one-percentage-point change in the corporate rate would give tax writers about $100 billion of revenues over a decade that could be used in many ways. One could be to repeal a federal tax on inheritances paid by wealthy Americans. Another might be to end the corporate alternative minimum tax.
Some Republicans also wanted a slightly higher corporate rate to pay for a higher child tax credit.
Lawmakers had also debated capping a popular individual deduction for mortgage interest at $750,000 in home loan value, instead of $1 million.
Trump is seeking to sign a tax bill by the end of the year to achieve Republicans' first major legislative victory since they took control of both chambers of Congress and the White House in January.
After his lunch with Republican lawmakers, Trump will speak on tax legislation alongside five middle class families who would benefit, senior administration officials said.
He wants to try to counter claims that the Republican tax plan would largely benefit corporations and the wealthy by saying it would also cut rates for lower- and middle-income taxpayers, who could see additional benefits, such as higher wages, the officials said.
The nonpartisan Joint Committee on Taxation and Congressional Budget Office have both concluded that wealthier taxpayers would disproportionately benefit from the Republican proposals. (Additional reporting by Steve Holland, Susan Cornwell, Richard Cowan, Makini Brice and Doina Chiacu; Editing by Kevin Drawbaugh and James Dalgleish)