The House Speaker issued her first public statement about the assault, highlighting that the hammer-wielding assailant was after her -- not her 82-year-old husband Paul -- but she was in D.C. at the time of the attack.

Nancy wrote ... "a violent man broke into our family home, demanded to confront me and brutally attacked my husband Paul. Our children, our grandchildren and I are heartbroken and traumatized by the life-threatening attack on our Pop. We are grateful for the quick response of law enforcement and emergency services, and for the life-saving medical care he is receiving."

Thanking her fellow members of Congress, Nancy stated their "prayers and warm wishes" have helped Paul progress in his recovery as his condition improves. She ended by quoting scripture from the Book of Isaiah.

As we reported ... Paul was violently attacked inside his family's San Francisco townhouse early Friday morning after David DePape forced his way inside through a back door, brandishing the hammer.

Paul surreptitiously called 911 from his cell phone and kept the line open so the operator could hear him talking in code to DePape while in clear distress.

Sensing something was wrong, the operator quickly phoned police dispatch and asked for a higher-priority response to the scene.

Within minutes, SFPD officers got to the townhouse only to find Paul and DePape fighting over the hammer. DePape allegedly seized control of the weapon and bludgeoned Paul, fracturing his skull.

Cops tackled DePape, disarmed him and placed him under arrest. DePape was booked into the San Francisco County Jail for burglary, attempted murder, assault with a deadly weapon and several other felonies.