DUBLIN, N.H. -- Sen. Ted Cruz (R-Tex.) on Friday declined to back fellow Texas Republican Sen. John Cornyn's bid for reelection in 2014, saying that he will probably steer clear of all races in which incumbents face primary challengers.

(David J. Phillip/AP) (David J. Phillip/AP)

Cruz called Cornyn a "good man" and a "friend," but would not back the Senate minority whip.

"I think it is likely that I am going to stay out of incumbent primaries across the country, either supporting incumbents or opposing incumbents," Cruz told reporters.

No formidable primary challengers have come forward to challenge Cornyn, the Senate's second-ranking Republican. But his campaign is taking the potential threat of one seriously.

In a statement, Cornyn said he agreed with Cruz that voters should be the ones deciding the outcome of the campaign.

"Senator Cruz has been a great addition to the U.S. Senate and I have enjoyed working with him, fighting for Texas and conservative principles. He and I agree that the only endorsements that matter are those of the Texas voters and I look forward to earning their vote in 2014," said.

Cruz said he thinks the 2014 map is "very favorable" for Republicans, and he plans to concentrate on playing offense. "My focus in 2014 is open seats and seats that are currently held by Democrats," he said.

As vice chairman of the National Republican Senatorial Committee, Cruz holds leading position in in a group tasked with electing Republican senators. He told The Washington Post in an interview earlier this month that believes the NRSC should stay out of primaries, but left the door open to endorsing on his own.

Cruz won his seat in the Senate last year by scoring a primary upset against Lt. Gov. David Dewhurst (R) , once viewed as the overwhelming frontrunner in the contest.

Cruz made his remarks at a media availability here before a New Hampshire Republican Party fundraiser he headlined. Friday was the first time Cruz traveled to the Granite State as a U.S. senator.

In his speech, Cruz encouraged Republicans to take a stand for their principles, as he touted a plan he is pushing to defund President Obama's signature health care law.

"Obamacare is the single biggest job killer in this country," Cruz said.

The trip to the first-in-the-nation primary state stoked further speculation about Cruz's presidential ambitions. Already this year, he's made two trips to Iowa and one to South Carolina, a pair of other early nominating states.

Cruz spurred a new round of talk about whether he might run for the White House when he released his birth certificate this week. The senator was born in Canada, leading some to suggest he may not be eligible to run for president. He born a U.S. citizen because he has an American mother. He said Monday he would renounce whatever right he has to Canadian citizenship.

Cruz brushed off presidential chatter here Friday, insisting as he has before that he is traveling the country to build support for defunding Obamacare.

Cruz defended his long-shot push, a plan that could trigger in a government shutdown. Cruz and about a dozen other conservative Republican senators have signed a letter circulated by Sen. Mike Lee (R-Utah) encouraging lawmakers not to support any appropriations or continuing resolution bills that dedicate even a penny to Obamacare. Cornyn initially signed onto the effort, but later removed his name.

Sen. Kelly Ayotte (R-N.H.) introduced Cruz. She has not signed onto Lee's plan to defund Obamacare.

Earlier in the day, Cruz met with GOP activists, an aide said. The Friday evening fundraiser was held at the home of Ambassador Joseph and Augusta Petrone, an influential GOP couple in New Hampshire politics.

Updated at 8:57 p.m.