MT. PLEASANT, SC - DECEMBER 7: (EDITORS NOTE: Retransmission with alternate crop.)  Republican presidential candidate Donald Trump speaks to the crowd at a Pearl Harbor Day Rally at the U.S.S. Yorktown December 7, 2015 in Mt. Pleasant, South Carolina. The South Carolina Republican primary is scheduled for February 20, 2016. (Photo by Sean Rayford/Getty Images)
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MT. PLEASANT, SC - DECEMBER 7: (EDITORS NOTE: Retransmission with alternate crop.) Republican presidential candidate Donald Trump speaks to the crowd at a Pearl Harbor Day Rally at the U.S.S. Yorktown December 7, 2015 in Mt. Pleasant, South Carolina. The South Carolina Republican primary is scheduled for February 20, 2016. (Photo by Sean Rayford/Getty Images)
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Story highlights

Donald Trump highlighted a poll Tuesday that showed his backers would support him as an independent

Trump has said he'd run for president as a Republican, not an independent, as long as he's treated "fairly" by the party

(CNN) —  

Donald Trump is bringing back the “independent” talk.

The Republican presidential front-runner has said he’d stick with the party, rather than launching an independent campaign for the presidency, as long as he is treated “fairly” in its nominating contest.

But after top Republicans and nearly the entire field of his presidential rivals condemned his recent proposal to ban Muslims from traveling to the U.S., Trump took to Twitter to remind them his loyalty only runs so deep.

He tweeted Tuesday: “A new poll indicates that 68% of my supporters would vote for me if I departed the GOP & ran as an independent.” He also linked to a USA Today/Suffolk University poll showing those results.

GOP Chairman Reince Priebus said in an interview Tuesday with the Washington Examiner that he disagrees with Trump’s proposal – the first time the party’s chief has publicly criticized a Trump proposal.

“We need to aggressively take on radical Islamic terrorism but not at the expense of our American values,” Priebus said.

On Monday evening, the Republican Party chairmen of the three early voting states also lambasted his proposal to ban all Muslims from entering the United States amid a spate of terror attacks.

In early September, Trump met with Priebus and signed a party loyalty pledge.

“The best way for the Republicans to win is if I win the nomination and go directly against whoever they happen to put up. And for that reason, I have signed the pledge,” Trump had said, holding up the paper. “So I will be totally pledging my allegiance to the Republican Party and for the conservative principles for which it stands.”

The pledge reads: “I, ________, affirm that if I do not win the 2016 Republican nomination for President of the United States I will endorse the 2016 Republican presidential nominee regardless of who it is. I further pledge that I will not seek to run as an independent or write-in candidate nor will I seek or accept the nomination for president of any other party.”

Former Florida Gov. Jeb Bush, one of Trump’s GOP primary opponents, criticized Trump’s tweet, saying an independent campaign would cement a Hillary Clinton victory. (Bush’s implication: A Trump independent run would split conservative voters between two contenders.)

Bush tweeted: “Maybe Donald negotiated a deal with his buddy @HillaryClinton. Continuing this path will put her in the White House.”

Republican leaders of the House and Senate and party chairs had criticized Trump for his proposal to ban Muslim travel to the United States.

Senate Majority Leader Mitch McConnell, R-Kentucky, said Trump’s “suggestion is completely and totally inconsistent with American values.”

House Speaker Paul Ryan, R-Wisconsin, told reporters Tuesday that “this is not conservatism.”

“Some of our best and biggest allies in this struggle and fight against radical Islam terror are Muslims,” Ryan said.