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Mr. Perez “has shown a glaring inability to tell the truth and dispassionately apply the basic constitutional tenet of ‘equal justice under law,’” the group said in a statement.

Much of the criticism surrounding Mr. Perez stems from an agreement he negotiated with the city of St. Paul, Minn., during his time at the Justice Department. Republican lawmakers accuse Mr. Perez of pressuring St. Paul officials to withdraw a housing discrimination lawsuit last year by agreeing to simultaneously drop a whistleblower case against the city.

The whistleblower case could have netted taxpayers nearly $200 million, but Mr. Perez dropped it because he was afraid of the possible precedent set by the city’s housing discrimination lawsuit. Critics say Mr. Perez overstepped his authority in this case.

“That seems to me to be an extraordinary amount of wheeling and dealing,” said Sen. Lamar Alexander of Tennessee, the ranking Republican on the committee, last month during Mr. Perez’s confirmation hearing. “It seems to me you’re manipulating the legal process.”

Opponents are also critical of Mr. Perez’s handling of a politically charged voter discrimination case against the New Black Panther Party. After the group was accused of scaring white voters away from the polls during the 2008 presidential election, Mr. Perez used his influence to pressure authorities to drop the case.

“He refused to protect the right to vote for Americans of all races,” Mr. McConnell said.

“Americans of all political persuasions have a right to expect that the head of such a sensitive federal department, whether appointed by a Republican or a Democrat, will implement and follow the law in a fair and reasonable way,” Mr. McConnell added. “But I do not believe they could expect as much from Mr. Perez.”