BAGHDAD, June 19 (Reuters) - Two days of fighting between gunmen loyal to Shi'ite cleric Moqtada al-Sadr and Iraqi police have killed 23 people and wounded 110 in the southern city of Nassiriya, a hospital doctor said on Tuesday. The clashes erupted on Sunday night when police attacked a Sadr office in Nassiriya in an apparent response to an attack on the head of police which wounded him. Nassiriya is one of Iraq's oil-rich cities and has been relatively calm until recent days.