The city, known as Tadmur in Arabic, is home to a UNESCO World Heritage site and the violence has fueled fears Islamic State will destroy ancient ruins. The offshoot of al-Qaida advanced into the city over the weekend but had been repelled.
Syrian state television, citing a military source, said in a news flash that armed forces had confronted "the Daesh (Islamic State) terrorist group" when it tried to enter a northern neighborhood of the city on Wednesday.
Palmyra's 2,000-year-old monuments, which lie on the south-western fringe of the modern city, were put on UNESCO's World Heritage in danger list in 2013. Islamic State has destroyed antiquities and ancient monuments in Iraq and is being targeted by US-led air strikes in both countries.
The Britain-based Syrian Observatory for Human Rights said the enemy sides were shelling each other in Palmyra and that the Syrian military had carried out air strikes.
Pictures posted by Islamic State supporters on social media showed gunmen in what they described as the streets of Palmyra, about 240 km (150 miles) northeast of Damascus.