The aim is to retake areas near Syria's northern border to Turkey, according to SDF.
Ruken Jamal, spokesperson for the Kurdish SDF-allied YPG militia's female branch, YPJ, says that their fighters are about seven miles from the border town of Manbij in northern Syria.
The town is currently controlled by SNA (Syrian National Army), which has close ties to Turkey. SDF reported clashes near the town on Monday.
Clashes between the Kurdish forces and SNA have escalated since Bashar al-Assad fell earlier in December.
The UK-based conflict monitor Syrian Observatory for Human Rights (SOHR) reports that SDF has retaken four villages near a strategically important dam in the area. According to SOHR, dozens of people from both sides have been killed since the fighting intensified.
"Syria is entering a new phase and discussions are underway about the country's future," says Jamal according to AP.
"Turkey is trying to distract us with attacks and exclude us from the negotiations in Damascus," she continues.
SNA was involved in the lightning-fast offensive that, under the Islamist group Hayat Tahrir al-Sham, overthrew dictator al-Assad, but has since continued to fight against SDF, which is considered one of Syria's key players going forward.
Turkey links SDF to the Kurdistan Workers' Party (PKK), which is labeled as a terrorist organization by Ankara.
Syria's Democratic Forces, SDF, have made up a large part of the resistance against the terrorist movement IS in Syria. SDF is dominated by the Kurdish YPG militia.
YPG (People's Defense Units) is the armed branch of PYD (Democratic Union Party), which is the largest political party among Kurds in Syria.
Turkey equates YPG and PYD with the Kurdistan Workers' Party PKK, which is labeled as a terrorist organization by Turkey, the EU, and the US after taking up arms against the Turkish state in the fight for independence.