In its statement, the PYD said 19 FSA members were killed in the clashes, while 40 PYD fighters also lost their lives. The PYD has also accused the KNC of driving a wedge between the FSA and the PYD.
However, in a statement the KNC noted that “the PYD's clashes with the FSA just simply serve the interests of the Assad regime.”
The London-based Syrian Observatory for Human Rights (SOHR) has meanwhile stated that some groups functioning under the umbrella of the FSA are violating human rights in the country. The general director of the SOHR, Rami Abdulrahman, said there is an authority gap in regions that used to be controlled by President Bashar al-Assad's forces.
The observatory also reported that more than 200 Kurdish civilians were detained over the weekend by militants.
Rebels in Aleppo have fought with Kurdish militants in recent days, accusing Syria's Kurds of siding with Assad. Many Kurds say they want to stay out of the violence by distancing themselves from either side.
The fighting in Aleppo's predominantly Kurdish neighborhood of Ashrafieh late Friday occurred a day after Syrian rebels pushed into largely Kurdish and Christian areas that have been relatively quiet during the three-month battle for the city. Kurdish groups have for the most part tried to steer a middle course in the conflict between the rebels and the Assad regime, while some figures have allied with the rebels, others with Assad, and others have remained neutral.
Mohieddine Sheik Ali, head of the Kurdish Yekiti party, told The Associated Press that the clashes broke out after rebels entered Ashrafieh, violating "a gentlemen's agreement" not to go into Kurdish areas in Aleppo.
He said there are 100,000 Kurds in Ashrafieh and many in the nearby Sheik Maksoud area. Sheik Ali said tens of thousands of Arabs have also fled to these areas from the violence in other parts of Aleppo.
The observatory said the clashes led to a wave of kidnappings between the two groups, but did not provide further details. Pro-government news websites also reported the clashes.
Kurds are the largest ethnic minority in Syria and make up around 10 to 15 percent of the country's 23 million people. Most of them live in the northeastern province of Hasakeh near the border with Turkey, but large neighborhoods in Aleppo as well as the capital Damascus are Kurdish-dominated.
After the anti-government uprising began in March last year, both the Syrian government and opposition forces began reaching out to the long-marginalized minority whose support could tip the balance in the conflict.