The Syrian Observatory for Human Rights monitoring group said nearly 300 people have been killed in four days of fighting since IS launched an assault on the desert oasis city on Wednesday.
The toll comprised 123 soldiers and loyalist militiamen, 115 IS fighters as well as 57 civilians, dozens of whom were executed by the jihadists, the Observatory said, quoting sources on the ground.
Yesterday the jihadists pressed their offensive and seized the northern part of the modern town of Palmyra, known as Tadmur in Arabic, but were driven out by regime forces.
He told AFP the army was "still combing the streets for bombs" after recapturing the northern districts.
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"The situation in the city and its outskirts is good," he said.
But the Observatory said clashes were still under way Sunday in the northern suburb of Al-Amiriyah, around the prison east of the city and around Haql al-Hail gas field northeast of Palmyra.
Observatory director Rami Abdel Rahman said the jihadists were still just a kilometre (less than a mile) away from the UNESCO-listed heritage site and its adjacent museum housing thousands of priceless artefacts.
Syrian antiquities chief Mamoun Abdulkarim expressed relief that IS, known for its wanton destruction of archaeological sites in territory it controls in Syria and Iraq, did not attack the site.
"We have good news today, we feel much better," Abdulkarim told AFP by telephone.
"There was no damage to the ruins, but this does not mean we should not be afraid."
The jihadists launched their offensive from their stronghold in the Euphrates Valley to the east, triggering ferocious fighting with the army, which has a major base just outside Palmyra.
Abdulkarim said he remained concerned for Palmyra in light of the destruction wreaked by IS on pre-Islamic sites such as Nimrud and Hatra in neighbouring Iraq.