The Syrian Democratic Forces (SDF) were formed in mid-October as an alliance between the powerful Kurdish People's Protection Units (YPG) and other Syrian rebel groups.
"This is the first step of the Syrian Democratic Forces," said Sherfan Darwish, spokesman for the Burkan al-Furat Arab rebel group, which is part of the SDF.
Speaking to AFP by phone from Syria, Darwish said the operation began on Friday night and would target IS-held areas in the northeast province of Hasakeh, including the towns of Shadadi and Al-Hol.
Darwish said the operation would receive air support from the US-led coalition striking IS in Syria since September 2014.
In a statement on its Facebook page the coalition later said that it had targeted IS tactical units and fighting posts outside Al-Hol on Friday.
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In a video statement published online, the YPG confirmed the beginning of the operation "with all of the members of the SDF, and with support from and coordination with the international coalition, to liberate the southern parts of Hasakeh province".
Clashes on Saturday raged between the SDF and IS outside Al-Hol and Al-Ghazayleh, said Rami Abdel Rahman, head of the Syrian Observatory for Human Rights.
Both of those areas lie northeast of Hasakeh city in a thin slice of Syrian territory between the Turkish and Iraqi borders.
Abdel Rahman said the SDF were backed on Saturday by air strikes from the US-led air coalition.
Most of Hasakeh province is divided in control between Kurdish forces and IS jihadists, although regime forces are present in some provincial cities including the capital.
In June, IS seized several neighbourhoods in Hasakeh city but was expelled a month later after battles involving both regime troops and Kurdish fighters.
The SDF announcement came a day after the White House said it would send "fewer than 50" special forces personnel to Syria's north, reversing a long-standing refusal to put US boots on the ground.