UPDATE 1-Trump expects another tax overhaul, says 'probably in October'

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WASHINGTON, June 29 (Reuters) - U.S. President Donald Trump said he expects a second tax overhaul to be unveiled in October or a bit earlier, and he is considering cutting the corporate tax rate to 20 percent from 21 percent.

In an excerpt of a Fox Business Network interview to be broadcast on Sunday, Trump said: "We're doing a phase two. We'll be doing it probably in October, maybe a little sooner than that."

"One of the things we're thinking about is bringing the 21 percent down to 20, and for the most part the rest of it would go right to the middle class," he said.

In December, Trump signed the biggest overhaul of the U.S. tax code in 30 years, slashing the corporate tax rate to 21 percent from 35 percent and giving temporary tax relief to middle-class Americans.

The sweeping bill passed the Republican-controlled Congress over the opposition of Democrats, who decried it as a giveaway to the wealthy that would add $1.5 trillion to the $20 trillion national debt.

Republicans, hungry to revisit the tax issue ahead of a November midterm election showdown for control of Congress, are already due to unveil the outline of new tax legislation over the summer in the House of Representatives.

But more tax cuts are unlikely to succeed in the closely divided Senate, where Democrats and conservative fiscal hawks could block such a measure.

The nonpartisan Congressional Budget Office warned this week that more tax cuts would hasten the growth of an already rapidly rising federal debt.

The debt, which equals 78 percent of U.S. gross domestic product, is on track to eclipse the 106 percent record set just after World War Two in 2034.

House Ways and Means Committee Chairman Kevin Brady, who presides over the chamber's tax policy debate, said this week that new legislation would aim to make permanent tax cuts for individuals that are due to expire in 2026. He expects a House vote in the autumn.

The Texas Republican made no mention of plans for an additional one percentage point cut in the U.S. corporate rate, which analysts say would reduce government revenues by an additional $100 billion over a decade. (Reporting by Eric Beech and David Morgan; Editing by Mohammad Zargham and Tom Brown)