Zdenko Turtak from Velka Ida, Kosice, pleaded guilty to those offences but denied attempted murder during a video link appearance at Leeds Crown Court.
He was charged in connection with an attack on a woman at a bus stop in Beeston Road on 6 March.
Prosecutors will decide within weeks whether to accept Turtak's pleas.
A 21-year-old man extradited from Slovakia has admitted the rape and grievous bodily harm of an 18-year-old woman in Leeds.