A group of Republican senators said Wednesday they will try to block President Obama’s choice to head the Social Security Administration until an investigation of a troubled computer contract is concluded.

All 11 Republican members of the Senate Finance Committee signed a letter to the nominee Wednesday. They said there is evidence that Social Security officials may have misled Congress and investigators about problems with a $300 million computer program that doesn’t work.

Obama nominated acting commissioner Carolyn W. Colvin to a six-year term in June. Colvin was deputy commissioner for 3 1 /2 years. She has been acting commissioner since February 2013.

“We cannot in good faith allow a nomination for any position that requires the advice and consent of the Senate to proceed to a vote as long as the specter of a potential criminal investigation surrounds the nominee and/or those in their inner circle,” wrote the senators, led by Sen. Orrin Hatch of Utah, the top Republican on the committee.

“Therefore,” the senators wrote, “it is essential to address your role with respect to this inquiry before each of us can make an informed decision on how to vote for your nomination once it reaches the full Senate for consideration.”

A Social Security spokeswoman said in an e-mail, “Carolyn W. Colvin is not personally the subject of any criminal investigation.”

“Agency representatives previously briefed members of the Senate and House regarding the issues raised in the Senate Republican Finance members’ letter,” agency spokeswoman LaVenia LaVelle said. “The acting commissioner will respond timely and fully to the members’ requests and continue to cooperate with Congress and any related investigation.”

LaVelle noted that the agency just received the senators’ letter Wednesday.

Social Security officials have acknowledged that the agency spent nearly $300 million on a computer project that doesn’t work. The agency, however, is trying to revive it. The program is supposed to help workers process and manage claims for disability benefits.

Six years ago, the agency embarked on an aggressive plan to replace outdated computer systems overwhelmed by a growing flood of disability claims. But the project has been racked by delays and mismanagement, according to an internal report the agency commissioned.

The project is in the testing phase. The agency can’t say when it will be operational or how much it will cost.

In the meantime, people filing for disability claims face long delays at nearly every step of the process — delays that were supposed to be reduced by the new processing system.

The Associated Press reported on the computer problems in July. In September, the Finance Committee voted 22-2 to advance Colvin’s nomination to the full Senate.

— Associated Press