WASHINGTON — A Senate panel’s scheduled vote this week could strain the already rancorous relationship between lawmakers and the CIA and pressure President Obama to step into the fray.

The Senate Intelligence Committee will weigh calling for the release of key sections of a voluminous report on terrorist interrogations, hoping to shed light on the most unsavory elements of the Bush administration’s war on terror after the Sept. 11, 2001, attacks.

Despite now serving Obama, the CIA maintains the report underestimates the intelligence value of waterboarding and other methods employed by intelligence officials at undeclared ‘‘black site’’ facilities overseas. But the differences between intelligence officials and Senate investigators have spiraled beyond the contents of the review.

The dispute became public two weeks ago as the committee chairwoman, Senator Dianne Feinstein, accused the CIA of improperly monitoring the computer use of Senate staffers and deleting files, and undermining the separation of powers between the executive and legislative branches.

The CIA and the executive branch hold the keys as final determiners of what ought to remain classified. Senators primarily have the bully pulpit of embarrassing the CIA publicly and the last-resort measure of going after the agency’s budget.

The president has refused thus far to weigh in on Congress’s dispute with the CIA, while pledging to declassify at least the findings of the Senate report ‘‘so that the American people can understand what happened in the past, and that can help guide us as we move forward.’’