* Rebels still control central districts of Homs city
* Rebel Hama offensive stalled by arms shortage -activist
* Palestinian who fought for Hamas killed in Aleppo
BEIRUT, Dec 29 (Reuters) - Syrian government forces have pushed rebels from a district in Homs after several days of fierce fighting in the strategically important city, opposition activists said on Saturday.
The army moved into Deir Ba'alba, a neighbourhood on the northeastern edge of Homs, they said, leaving the rebels controlling just the central neighbourhoods around the old city and the district of Khalidiyah, immediately to the north.
Homs, in central Syria, was the scene earlier this year of some of the heaviest fighting in the 21-month uprising against President Bashar al-Assad which has killed at least 45,000 people, according to activist tallies.
On the junction of roads linking Assad's power base in Damascus to the heartlands of his Alawite minority in the port city of Tartous and Latakia province, Homs has strategic value in his battle with the mainly Sunni Muslim rebels.
There were unconfirmed reports that dozens of fighters had been killed in the battle for Deir Ba'alba, the director of the British-based Syrian Observatory for Human Rights, Rami Abdelrahman, said.
Rebels have been gaining ground in recent months, particularly in the northern provinces of Aleppo and Idlib, and launched an offensive in the central Hama province which would extend their control south towards Homs and Damascus.
But an activist in Hama province said on Saturday that the army had reinforced its positions in the town of Morek, which lies on the main north-south highway linking Damascus to Aleppo, to push back rebels who were running low on ammunition.
A rebel attack on the military base of Wadi Deif, further north on the same highway, had also slowed as rebels struggled to maintain supplies, the activist who used the name Ali al-Idlibi told Reuters by Skype.
He also said Assad's forces had bombarded the provincial town of Karnaz in Hama on Saturday, killing 10 people. Other activists said 12 people were wounded, with no fatalities. It is not possible to verify reports from Syria because authorities restrict media operations in the country.
Activists also said a Palestinian fighter who had been a prominent figure in the armed wing of the Palestinian militant group Hamas was killed in Aleppo province on Friday.
Mohammed Qanita was killed in fighting around Aleppo airport where he had been helping to train Arab and Muslim fighters, a rebel said.
A Hamas source in Gaza said Qanita had left the Qassam Brigade of Hamas and joined a jihadi group before leaving for Syria to fight there.
The exiled leadership of Hamas was based in Damascus until earlier this year, when officials from the Sunni Islamist movement, which sympathises with the uprising against Assad, quietly pulled out.