D.C. Mayor Vincent C. Gray said Thursday that he will request a federal disaster declaration Friday to help pay for repairs to city facilities and Washington National Cathedral in the wake of the Aug. 23 earthquake.

Officials said that if the request is granted, the District would probably ask the Federal Emergency Management Agency for $7 million to make repairs in the city and $15 million for the cathedral.

Speaking after a tour of the damaged cathedral, the mayor said that the towering English gothic edifice in Northwest is an “irreplaceable national treasure” and an institution that transcends religion.

Asked whether it is proper for the government to pay for repairs to a religious structure, he said, “This is far more than a religious institution.” The National Park Service awarded a $700,000 matching grant to the cathedral last year. “There is a precedent for this,” he said.

Cathedral officials have said they need to raise at least $15 million for initial repairs, and the chief stone mason there thinks overall repairs could take a decade. More than $1 million has been spent on stabilization, an official said.

The mayor said that city buildings — including the Wilson Building and the D.C. government headquarters, where floorboards buckled on the sixth floor — were also damaged.

The cathedral has been closed as workers stabilize or remove large stone pinnacles and other decorative elements shaken from their foundations during the quake.

Many of the larger pieces have been removed from the three towers and lowered into a flatbed truck on the grounds. The chief stone mason, Joseph Alonso, said the towers had been stabilized.

Officials hope to reopen the cathedral Nov. 12.

Cathedral officials have said that they need to raise $25 million — $15 million for short-term repairs and $10 million to help pay for cathedral operations — through the end of 2012.

Cathedral officials said that operations are not funded by the government or a national church entity. Located at Massachusetts and Wisconsin avenues NW, the 301-foot-tall edifice is one of Washington’s most iconic and visible buildings.