Republican presidential candidate Donald Trump will continue his individual negotiations with television networks over his demands for the upcoming GOP debates, his campaign confirmed to CBS News.

However, the campaign declined to clarify whether Trump will sign the letter that nearly all of the GOP campaigns collectively drafted over the weekend to list their demands.

"We are going to work with everyone but continue to negotiate with the networks," The Trump campaign said Monday.

• The GOP campaigns list their demands for networks
• Hispanic Caucus to NBC: Disinvite Trump as SNL host

Meanwhile, a few other candidates said Monday they will not sign the letter: New Jersey Gov. Chris Christie, former Hewlett-Packard CEO Cary Fiorina, and Ohio Gov. John Kasich.

Kasich's and Fiorina's campaigns both suggested that the demands in the letter were petty. The letter demanded, among other things, that the debate hall be kept no warmer than 67 degrees, that the campaigns get pre-approval of any graphics, and that the debate moderators let the campaigns know ahead of time whether any questions will come from the audience.

Kasich spokesman Chris Schrimpf said in a statement that as governor of Ohio, Kasich is "used to answering tough questions all the time." After a town hall in Des Moines, Iowa on Monday, Kasich said one of his staffers was at the meeting on Sunday during which the campaigns discussed the letter. However, he added, "I really have not given it any thought, that is all a process. Other people think about that. I don't."

Meanwhile, a Fiorina staffer sent a letter to GOP attorney Ben Ginsberg -- who helped draft the letter of demands -- explaining why Fiorina is not signing it.

"These debates are an important chance for voters to see conservative candidates under pressure and over time," staffer Sarah Isgur Flores wrote. "We have consistently and successfully discussed our concerns with the networks and the voters--and not behind closed doors like the political class seems to like to do."

Isgur Flores noted that the Fiorina has called for some changes to the debates. However, she wrote, "We do not care whether it's 67 degrees or our green room isn't as plush as another candidate."

Current GOP front runner Ben Carson responded Monday to the news that Trump would continue negotiating with networks on his own: "The important thing is that we have an influence on the debate process and be able to do something that actually makes sense, that disseminates appropriate information to the voters so they can make an intelligent decision," he said during a book tour stop in The Villages, Florida.