Iran has been one of President Bashar Assad's strongest backers and has, along with Lebanon's Iran-backed militant Hezbollah group, sent fighters to battle on the government's side.
Iran's semi-official Fars news agency quoted Hossein Ali Rezaei, a spokesman for the Revolutionary Guard in the northern province of Mazandaran, as saying that 13 members were killed and 21 were wounded.
Rezaei did not say when or where the incident occurred but another semi-official news agency, Tasnim, quoted a Revolutionary Guard spokesman in the same area as saying that they were killed when a coalition of insurgents, including al-Qaida's branch in Syria known as the Nusra Front, seized the northern village of Khan Touman from pro-government forces.
Khan Touman was captured Friday after two days of intense clashes that also left dozens of Syrian militants dead, according to opposition activists.
The town was captured by a coalition known as Jaish al-Fatah, or Army of Conquest, an ultraconservative group led by the Nusra Front, and the jihadi militias Jund al-Aqsa and Ahrar al-Sham.
The announcement in Tehran came as a senior Iranian official met with Assad in Damascus and vowed continued support for his government in the country's five-year-old civil war.
Ali Akbar Velayati, an adviser to Iran's Supreme Leader Ayatollah Ali Khamenei, was quoted by Syria's state news agency SANA as saying that Tehran will always stand by Syria because it "knows that terrorism does not target Syria but the whole people of the region."
Iran and Russia have backed Syria throughout the conflict. All three refer to all those fighting to overthrow Assad as terrorists.
Also Saturday, a fragile cease-fire in the northern Syrian city of Aleppo has been extended for 72 hours, Russia said, as the Islamic State group battled other militant factions near the city.
The Russian Defense Ministry said the extension was made at Moscow's initiative and would also apply to the coastal province of Latakia. The cease-fire will now last until 12:01 a.m. on Tuesday (9:01 p.m. GMT Monday).
Russia and the U.S. last week reached an agreement to extend Syria's cease-fire to Aleppo, which had seen days of heavy fighting that killed 286 civilians, including 57 children, according to the Syrian Observatory for Human Rights, a Britain-based monitoring group.
The Syrian military had earlier said the cease-fire in Aleppo would last only 48 hours.
The Russian military accused the Nusra Front of attempting to destroy the cease-fire by carrying out attacks on Aleppo and trying to impose a blockade on the city from the south.
The Nusra Front and IS are not included in the cease-fire.
The Observatory and the other groups said Aleppo was relatively quiet after the cease-fire was extended, but reported heavy fighting between IS and other militant groups in the northern parts of Aleppo province, near the border with Turkey.
The Observatory, which relies on a network of activists inside Syria, said IS captured two villages in the region in clashes that killed least 12 extremists. The Local Coordination Committees, an activist-run collective, said the fighting is now concentrated near the northern villages of Dalha, Harjaleh and Hiwar Kilis.
Karimi reported from Tehran, Iran. Associated Press writer Bassem Mroue in Beirut contributed to this report.
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