The Kurds have long been one of the most effective foes of the Islamic State group, a reputation they burnished in recent months by repelling a months-long IS assault against the town of Kobani on the Turkish frontier.
The US-led coalition carried out hundreds of airstrikes that helped the Kurds break the IS siege in January.
Today's fighting focused in Hassakeh province in the extreme northeast of Syria, where IS militants took at least one village near the small town of Tal Tamr, the Britain-based Syrian Observatory for Human Rights and the Local Coordination Committees activist collective said. Tal Tamr is some 85 kilometers (50 miles) southwest of the provincial capital of Qamishli.
The IS gains came a day after Kurdish militiamen from the People's Protection Units, or YPG, captured around 20 villages southeast of Qamishli in a new offensive against the Islamic State group.
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Heavy fighting broke out again today, activists said.
The US military said coalition aircraft carried out 11 airstrikes against IS in Hassakeh yesterday.
In a statement released today, it said the air raids hit 10 IS tactical units and destroyed two IS vehicles, a bunker and a fighting position.
Also today, an explosion at a checkpoint near the Damascus suburb of Sayeda Zeinab killed six people, the state news agency said. Sayeda Zeinab is home to a key Shiite Muslim shrine.