Sen. Ted Cruz (R-Tex.) said he has no interest in signing a letter of demands surrounding debates that presidential campaigns are crafting to send to television networks.

Appearing on "The Kelly File" on Fox News, Cruz said he is "happy" to debate the candidates any time but is not interested in the letter.

"I'm not interested in signing onto a letter of demands," Cruz said.

Republican campaigns huddled in a suburban Washington hotel last weekend, trying to hammer out a three-page letter of possible demands after last week's debate on CNBC. Businessman Donald Trump decided to break off from the group and deal directly with the networks.

Read: Trump's campaign says he'll deal directly with TV networks on debates

Cruz reiterated his assertion that only journalists who have voted in a Republican primary should moderate the primary debates, because he said most journalists are "liberal Democrats." Host Megyn Kelly pushed back, arguing that fair journalists might be excluded under Cruz's rules.

"Would we have to submit our voting records to you or some committee?" she asked.

She cited two colleagues, Brett Baier and Chris Wallace. Cruz said he is confident they have voted in a Republican primary. Kelly asked if Cruz would participate in a debate hosted by the late Tim Russert of NBC, who worked for Democrats but was respected as a journalist by members of both parties. Cruz said he goes "on liberal shows" all the time but feels a conservative should moderate a primary debate.

New Jersey Gov. Chris Christie, another candidate for the Republican nomination, also appeared on Kelly's show and again said he refused to sign the letter.

"It's stupid," Christie said. "I don't care who the moderators are . . . my job is to listen to the questions, answer the questions, and if I don't like them call them out."