Sen. John Cornyn, the Senate's second-ranking Republican leader, faces tea party-backed Rep. Steve Stockman in Tuesday's election. Cruz declined to tell reporters how he plans to vote.
"I am not supporting any of the senators from my party, or their opponents" in this year's primaries, Cruz said, adding that he might change his mind later.
Cruz, a tea party favorite and potential 2016 presidential candidate, has infuriated fellow Republicans by forcing uncomfortable votes on issues such as the debt, and by raising money for conservative groups trying to defeat veteran Republicans, including Senate Minority Leader Mitch McConnell of Kentucky.
Cruz's comments are especially notable because he is a vice chairman of the GOP committee tasked with winning Senate elections. He criticized the committee's track record and policy of virtually always backing incumbents.
At a breakfast sponsored by Politico, Cruz said he is no longer writing fundraising letters for anti-establishment groups such as the Senate Conservatives Fund. McConnell's backers are angry at the group for supporting his tea party challenger, Matt Bevin, in Kentucky's May 20 primary.
Still, Cruz sharply criticized McConnell's leadership, and praised the Senate Conservatives Fund by name.
"The brightest stars in the Republican Party," he said, were opposed by "the Republican leadership in Washington" and backed by groups such as the conservatives fund.
"Washington insiders have a terrible record at picking winners and losers," Cruz said.
Senators typically back party colleagues for re-election. Serious primary challenges were rare until tea party activists ousted some GOP veterans in 2010 and 2012. Other Republican senators steered farther right to protect themselves from similar fates.
Cruz had few kind words for McConnell, who hopes to become Senate majority leader if Republicans gain six net seats this fall.
"I strongly disagree with some of the decisions the Republican leadership has made," Cruz said. He said McConnell is the party leader because "that is what is stenciled on his door."
Cruz infuriated McConnell's allies this month by threatening to filibuster a proposed increase in the federal debt ceiling. His actions forced several GOP senators to vote to clear the way for the increase, lest the party be blamed for a possible economic crisis.
McConnell and Cornyn, the Senate Republicans' top two leaders, were among those casting the unpleasant votes and drawing immediate criticism from tea partyers back home.
Also Thursday, House Speaker John Boehner, R-Ohio, noted the fifth anniversary of the tea party uprising.
"I have made it clear that I have great respect for the tea party and the energy they brought to the electoral process," Boehner told reporters. "My gripe is with some Washington organizations who feel like they've got to go raise money by beating on me and others."
The Tea Party Patriots marked the fifth anniversary of the grassroots movement at a Washington event. Sen. Rand Paul, R-Ky., drew laughs with a good news-bad news pairing: "The government is open, and the government is open."
He urged the group to offer an upbeat message and avoid name-calling.
Some tea party activists expressed disillusionment with GOP congressional leaders. Viveca Stoneberry of Spotsylvania, Va., said Boehner and others "pretend to be on the side of conservatives."
The exchanges came as establishment Republicans are pushing back aggressively against Senate tea party challengers in Kansas, Kentucky, Mississippi and elsewhere.
In Colorado, a political deal announced this week results in Ken Buck, a tea party-affiliated Republican who lost a close Senate race in 2010, dropping a similar bid this year, and running for the House instead. Replacing him in the Senate race against Democratic Sen. Mark Udall is Rep. Cory Gardner, who is more palatable to the GOP mainstream.
In Kansas, the Tea Party Express endorsed Milton Wolf, who opposes three-term Sen. Pat Roberts in the Republican primary.