Story highlights Trump didn't mention any Republican candidates by name

Kasich hasn't announced yet whether he will attend next month's GOP convention

(CNN) Donald Trump on Wednesday said his former Republican primary rivals who have refused to support him in November should be barred from running for public office again.

"They signed a pledge saying they will abide, saying they will back the candidate of the party," Trump said during a campaign appearance in Bangor, Maine, adding, "They broke their word. In my opinion, they should never be allowed to run for public office again because what they did is disgraceful."

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Trump didn't mention any Republican candidates by name. But some of his significant primary challengers, including Texas Sen. Ted Cruz , former Florida Gov. Jeb Bush and Ohio Gov. John Kasich -- who on Wednesday released a letter on his campaign fundraising list highlighting a positive poll for him -- have yet to endorse Trump despite saying during the primary they would back the GOP nominee.

Trump called Republicans who wouldn't back the pledge "sore losers."

Trump has struggled to unite Republican officials behind his campaign since clinching the party's nomination in early May and his frustrations with the slow pace of that unity have boiled over in recent weeks.

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