"Our forces entered the city of Raqqa from the eastern district of Al-Meshleb," SDF commander Rojda Felat told AFP.
She said fierce clashes were also raging on the northern outskirts of the city.
The Syrian Observatory for Human Rights said that the SDF had seized a number of positions inside Raqqa on Tuesday after advancing to the city's eastern edge overnight.
"They have taken control of a checkpoint in Al-Meshleb, as well as a number of buildings," Observatory head Rami Abdel Rahman told AFP.
"The advance came after heavy air strikes by the US-led coalition," he said.
The coalition has backed the SDF's seven-month drive for Raqqa with military advisers and weapons deliveries as well as air support.
After months sealing off access routes to the city from the east, north and west, the SDF on Tuesday announced a new phase in their fight for Raqqa.
"We declare today the start of the great battle to liberate the city of Raqqa, the so-called capital of terrorism and terrorists," SDF spokesman Talal Sello told reporters in the village of Hazima, north of the city.
"With the international coalition's warplanes and the state-of-the-art weapons they provided to us, we will seize Raqqa from Daesh," Sello told AFP, using an Arabic acronym for ISIS.
He asked civilians inside the city to keep away from ISIS positions and from the front lines.
As the SDF has drawn closer to the city, reports of civilian casualties in coalition air strikes have swelled.
On Monday, the Observatory said a coalition bombing raid killed 21 civilians as they tried to escape Raqa by dinghy on the Euphrates River.
The same route had been used by ISIS fighters, Abdel Rahman said.
More than 320,000 people have been killed and millions more have fled their homes since the civil war erupted in Syria in March 2011.