Republican senators vowed Thursday to block any nominee to lead the fledgling Consumer Financial Protection Bureau unless stronger limits are put on its power, in the latest blow in a long-running battle to rein in the watchdog agency before it officially launches this summer.

In a letter to President Obama, 44 lawmakers called for a board of directors to run the agency, rather than a single leader. The letter also demanded tougher oversight of the CFPB by existing banking regulators, such as the Financial Stability Oversight Council, and that the new agency be funded by congressional appropriations. Under the current structure, the CFPB’s budget is carved from the Federal Reserve.

“How the CFPB director exercises his or her authority . . . will have a profound influence on the future of our economy and job creation,” the letter said. Lead signatories were Senate Minority Leader Mitch McConnell (R-Ky.) and Sen. Richard C. Shelby (Ala.), ranking Republican on the Senate banking committee.

The proposals mirror three bills passed by the House Financial Services Committee a day earlier. Rep. Sean P. Duffy (R-Wis.), who sponsored one of the bills, said he believed that “the movement here on both sides of the aisle is to make sure we have a system that’s going to work for our consumers.”

But consumer advocacy groups lashed out at the proposals, arguing that they would give banks undue influence over the CFPB and jeopardize its independence.

“Enactment of these measures would virtually guarantee that the CFPB would be a weak and timid agency,” said Travis Plunkett, legislative director for the Consumer Federation of America.

In response to the letter, a spokeswoman for the White House reiterated the need for an independent watchdog. Obama is under pressure to name a director for the agency before it opens for business July 21.

Harvard law professor Elizabeth Warren, in charge of setting up the CFPB, is considered a leading candidate, but she is disliked by many Republicans and financial industry officials. Any nominee will face a tough confirmation battle in the Senate. The president could appoint a head while the Senate is in recess, but that person would only be allowed to stay in the position until next year.

“Republicans in Washington may want to use revisionist history, but Americans haven’t forgotten that the recession was caused in part by predatory lenders and bad actors on Wall Street,” said Senate banking committee Chairman Tim Johnson (D-S.D.).