UPDATE 1-Tiff with Corker won't hurt tax push, plan changes coming -Trump

(Adds quotes from Trump, background on taxes)

WASHINGTON, Oct 10 (Reuters) - President Donald Trump said on Tuesday that his Twitter dispute with Republican Senator Bob Corker would not harm his administration's and congressional Republicans' push to overhaul the tax code and vowed to strengthen the party's tax plan.

In remarks that raised new uncertainties about the barely two-week-old plan, Trump said adjustments to it were coming within weeks. Asked if his spat with Corker would affect the tax effort, he said, "I don't think so, no."

The president has been feuding for days with the Tennessee Republican senator, who chairs the Senate Foreign Relations Committee and is the Senate's most outspoken "deficit hawk." He has vowed to oppose tax changes that expand the federal deficit.

Corker's position on taxes matters because Republicans control the Senate by only a narrow 52-to-48 margin. If Democrats oppose a tax overhaul, Trump can only afford to lose two members of his own party and still pass tax legislation.

After days of back-and-forth, on Tuesday the president referred to the senator as "Liddle' Bob Corker" in a tweet and said he had been made to "sound a fool" by the New York Times.

Corker said in an interview with the paper that Trump risked setting the nation on a "path to World War Three."

The president did not focus on that dispute during his reply in the Oval Office, instead noting that tax reform was politically positive and desired by Americans.

"People want to see tax cuts, they want to see major reductions in their taxes, and they want to see tax reform, and that's what we're doing," he said.

"And we'll be adjusting a little bit over the next few weeks to make it even stronger. But I will tell you that it's become very, very popular."

Asked to clarify Trump's comments about making the plan stronger, a White House spokeswoman said the administration had always planned to work with Congress to make the proposal one that people could get behind. (Reporting by Jeff Mason; Editing by Kevin Drawbaugh and James Dalgleish)