Washington, Aug 11 Controversial Republican presidential frontrunner Donald Trump and Fox News channel have struck an uneasy truce with an unapologetic real estate mogul sticking to his guns over his \"offensive\" criticism of a female channel host.

Fox News chairman Roger Ailes claimed Monday after a \"blunt but cordial conversation\" with Trump that \"the air has been cleared\" even as he stood by host Megyn Kelly, who had earned Trump\'s wrath with her questioning during Thursday\'s presidential debate.

\"We discussed our concerns, and I again expressed my confidence in Megyn Kelly. She is a brilliant journalist and I support her 100 percent,\" he said.

\"I assured him that we will continue to cover this campaign with fairness & balance. We had a blunt but cordial conversation and the air has been cleared,\" Ailes added.

Kelly briefly acknowledged the controversy on her 9 p.m. programme. \"I certainly will not apologize for doing good journalism\" she said in a pointed response to Trump, who had suggested earlier in the day that she should apologize to him.

Trump who has been lambasting Kelly and Fox for days over his \"unfair\" treatment at the hands of Fox moderators during Thursday night\'s Republican presidential debate.

He was particularly hard on Kelly saying there was\"blood coming out of her eyes, blood coming out of her wherever.\"

But after Ailes called, Trump tweeted that the Fox chief had assured him of this: \"\'Trump\' will be treated fairly on Fox News.\" Trump added: \"His word is always good!\"

Meanwhile, Democratic frontrunner Hillary Clinton mocked Trump as the Republican presidential field\'s shock jock, but said other candidates\' positions on women\'s rights are more offensive.

\"Yes, I know it makes great TV. I think the guy went way overboard-offensive, outrageous, pick your adjective,\" Clinton said of Trump after a town hall meeting in New Hampshire, the first primary state.

Clinton also suggested that she isn\'t taking Trump seriously. \"It\'s entertainment. It\'s all entertainment. I think he\'s having the time of his life,\" she said of Trump.

But business magnate Warren Buffett said Monday that Trump has a solid base of support in the race for the Republican presidential nomination that seems unshakable by his over-the-top comments.

Trump will have a block of delegates when the convention arrives, but with the huge field of Republican candidates, it\'s possible no one will have a majority, Buffett told CNBC.

\"I wouldn\'t be surprised if [Trump] maintained a quite a solid base for some time,\" Buffett said-adding that he won\'t run out of money.

Contrary to commentators\' suggestions that Trump\'s \"blood\" remarks would unravel his campaign, Trump remains at the top of the Republican field among would-be Republican primary voters, according to the latest NBC News Online Poll conducted by SurveyMonkey.

Trump and Fox News call a truce