Russia said its jets had helped force the militants out of the city center overnight, and its allies in the Syrian army were now fighting off another assault by the hardline Islamists.
But a news agency linked to Islamic State said it had only briefly retreated and was now back in control of Palmyra, an account backed by the British-based Syrian Observatory for Human Rights, which monitors the conflict.
Forces allied to Syria's government first recaptured the city from Islamic State in March, a victory held up as a major turning point in the war and the biggest reversal for the militants since Russia's intervention on the side of the government.
But Islamic State militants launched a surprise advance on the city on Thursday, taking control of nearby oil and gas fields, and pushing towards an airbase used by Russian forces, the Observatory said.
Russia's Defense Ministry said its jets had launched 64 strikes and killed more than 300 militants overnight, helping the Syrian army push the main force back.
More than 4,000 Islamic State militants had since regrouped and launched a second attack on Sunday, Russian news agencies cited Russia's monitoring centre in Syria as saying.
"Despite heavy losses in manpower and equipment, the terrorists are trying as hard as possible to secure a foothold inside the city," Interfax quoted a statement from the center as saying. "Syrian troops are fighting to defend Palmyra."
Syria's army acknowledged there was a large offensive by the militants from several fronts near a major grain silo 10 km (6 miles) east of the city.
An Islamic State recapture of Palmyra would be a major reversal for Syria's government and its Russian backer which hailed the city's capture in March, sent troops to protect it and even staged a concert there.
The fight could also have implications for other battlegrounds in Syria.
The Syrian army said on Saturday it had sent reinforcements to Palmyra to help defend it. Some of those were diverted from Aleppo, a rebel from the countryside outside that northern city said, a development that could ease pressure on rebels there.