ALEPPO, Syria — Syrian warplanes, artillery and mortar rounds pounded areas in eastern Aleppo on Saturday drawing rebel rockets, as government troops gain new ground in the shrinking opposition-held enclave.

After four years of holding nearly half of the divided city, rebel fighters have been increasingly squeezed into the center of the eastern enclave. Government and allied troops, including Lebanese, Iraqi and Iranian fighters, have concentrated their fight on the northeastern part of the enclave, swiftly taking new districts since their offensive began last week. Another front on the southern outskirts of the city has been slower, as rebel fighters push back government advances there.

The advances have caused massive displacement.

The U.N. estimated that more than 31,000 have already fled their homes, either to government or Kurdish areas, or deeper into the besieged enclave. The fighting has also intensified the rebel shelling of government-held areas in Aleppo.

The state broadcaster al-Ikhbariya said “precise operations” by government and allied troops aim to rout out “terrorists,” which is how the government refers to all armed opposition groups.

The sound of war prevailed in the city early Saturday. Warplanes made several runs overhead, drawing what appeared to be rebel machine gun fire toward the aircraft.