* 51 soldiers executed this week - monitoring group
* Rebels take isolated, rural army outposts
* Army advances into Homs city
BEIRUT, July 26 (Reuters) - Syrian rebels say they have overrun army positions in the north and south of the country this week, including an offensive in which a rights monitoring group said 51 soldiers were executed.
Insurgents have focused on taking isolated army outposts, mostly in rural areas while forces loyal to President Bashar al-Assad have made gains in recent months around the capital Damascus and the central city of Homs.
One video, posted on YouTube on Wednesday by a rebel group calling itself the Supporters of the Islamic Caliphate, shows around 30 bodies of young men piled up against a wall. Blood is splattered on the wall and one corpse is smouldering.
"Tens of Assad's (militia) killed," says a man off camera. He said the footage was filmed in the area of the northern town of Khan al-Assal which was taken by rebels last week.
The Syrian Observatory for Human Rights, an anti-Assad monitoring group, cited activists on Friday in Khan al-Assal who said that more than 150 soldiers were killed on Monday and Tuesday in and around the town.
The Observatory said that figure included 51 soldiers and officers who were executed.
Another video, posted by a rebel group in the village of Hara in the southern province of Deraa, shows several dead soldiers in a room, lying in a pool of blood with head injuries.
"These are Assad's dogs," says a voice off screen.
The United Nations says more than 100,000 people have died in the Syrian uprising since March 2011, which turned into an armed insurgency after the authorities used force to suppress peaceful street protests. Ancient buildings and artefacts across the major Arab state have been destroyed in the fighting.
Assad's forces have been on the offensive since last month when the army, backed by militants from the powerful Lebanese guerrilla group Hezbollah, recaptured a border town near Lebanon straddling supply lines between Damascus and Syria's seacoast.
Both sides are accused by rights groups of abuses, including executing enemy combatant, and the war - pitting Sunni majority rebels against Assad's own Alawite sect and Shi'ite Hezbollah - has descended into sectarian hatred.
State news agency SANA reported on Thursday that "army units have made considerable headway in the battle against the armed terrorist groups in al-Khalidiya neighbourhood in Homs city."
It said the army had killed scores of "terrorists" in Homs, where whole districts have been razed by two years of conflict, with neither side ever fully taking over the city.
Assad's forces also clashed with rebels on the outskirts of the capital on Friday. A resident of Damascus said warplanes were targeting the northern Barzeh district.
"People close to Barzeh say the sonic booms and subsequent bombardment blasts have been unrelenting all day," she said. (Reporting by Oliver Holmes; Editing by Jon Boyle)