WASHINGTON  Seven former directors of the Central Intelligence Agency asked President Obama on Friday to shut down the new Justice Department inquiry into past abuses during interrogations of terrorism suspects, arguing that it “will seriously damage” the nation’s ability to protect itself.

In a letter to Mr. Obama, the former C.I.A. chiefs said the cases under study had already been examined by career prosecutors who found that no criminal charges were warranted. To reopen cases based on a change in which political party controls the government, they wrote, will make it harder for intelligence officers to take risks without worrying that some future attorney general might investigate them.

“Those men and women who undertake difficult intelligence assignments in the aftermath of an attack such as September 11 must believe there is permanence in the legal rules that govern their actions,” the men said in their letter.

They argued that the new inquiry would result in the disclosure of information about past operations that “can only help Al Qaeda” elude capture, and would convince foreign intelligence agencies that they could not trust the United States to protect secrets.