A man sexually assaulted and tried to rape an 81-year-old woman in the stairwell of her Tribeca apartment building Thursday afternoon, cops said.

The thug followed her into the elevator of the Beekman Street building shortly before 1 p.m.

He pushed her into a stairwell, and sexually assaulted her and attempted to rape her, but fled after she struggled, cops said.

The woman declined medical attention at the scene.

No arrests have been made. Cops described the suspect as a 20-year-old man, 5-foot-6 and 150 pounds.