WASHINGTON (Reuters) - Republican Jeb Bush's support is slipping in the race for the party's presidential nomination, and front-runner Donald Trump has opened a 20-point lead over his closest rivals, a Reuters/Ipsos opinion poll showed on Tuesday.

Republican backing for Bush dipped from 16 percent to 8 percent in the last five days, the online poll found, as the former Florida governor feuded with Trump over immigration policy and defended his use of the term "anchor babies" to describe U.S.-born children of illegal immigrants.

Trump's support remained largely unchanged over the last week at about 30 percent, well ahead of the 17-strong pack seeking to represent the Republican Party in the November 2016 presidential election.

Bush fell into a third-place tie with retired neurosurgeon Ben Carson in the poll, and former Arkansas Governor Mike Huckabee moved into second place with 10 percent.

Bush's dip came as he battled Trump over immigration in recent days, calling the real estate mogul's hard-line plan to deport undocumented immigrants and construct a wall on the Mexican border costly and unrealistic.

Bush also was forced to defend his use of the term "anchor babies," which some consider offensive, in a radio interview last week. Trump gleefully punched back with tweets that called Bush's efforts to explain himself "clumsy" and "a mess."

"Bush's numbers have been trending down, generally, and he has just been overshadowed by Trump," said Ipsos pollster Chris Jackson. "His argument that he will be the establishment's guy in the race is looking less and less convincing."

Trump's continued appeal has confounded the Republican establishment, which has been anxiously waiting for the party's primary voters to grow weary of his style.

Instead, Trump's support in the poll has largely held steady or grown, fueled by his image as a maverick who speaks his mind and stands up to authority.

The poll found about 77 percent of Republicans said Trump is appealing because he is not interested in being "politically correct," and about the same number said he is appealing because he confronts the media. About 68 percent said he was appealing because his personal fortune meant he was not indebted to donors.

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Big majorities of Republicans now say Trump's participation in the party's presidential debates will challenge the establishment and open the party to new ideas.

The results in Tuesday's rolling poll are based on 511 Republicans and have a credibility interval of plus or minus 5 percent.

(Reporting by John Whitesides; Editing by Lisa Shumaker)