The Syrian Democratic Forces now control "more than 70 percent of Tabqa," the Syrian Observatory for Human Rights monitor said.
Observatory director Rami Abdel Rahman said: "The Old City has been entirely taken and there is fierce fighting going on at the gates of the new town."
He said the alliance was bombing IS positions in the new town.
The SDF published photos Sunday it said showed items retrieved from newly captured parts of the town, including at least a dozen guns, as well as missiles, ammunition, and an IS flag.
The SDF entered Tabqa on Monday as part of their offensive against Raqa, IS's de facto Syrian capital.
Supported by US-led coalition air strikes and special forces advisers, the SDF surrounded Tabqa in early April.
The town sits on a strategic supply route about 55 kilometres (35 miles) west of Raqa, and served as an important IS command base, housing the group's main prison.
It is also adjacent to the Tabqa dam, another important strategic prize which remains under IS control.
The assault on Tabqa began in late March when SDF forces and their US-led coalition allies were airlifted behind IS lines.
The city is home to an estimated 85,000 people, including IS fighters from other areas.
IS has put up fierce resistance, including using weaponised drones, a tactic the group perfected in neighbouring Iraq.
The group is also fighting street-to-street and using suicide attackers and car bombs to slow the SDF's advance, according to the Observatory.
The assault on Raqa, dubbed "Wrath of the Euphrates", was launched in November and has seen SDF fighters capture large swathes of countryside around the city.
More than 320,000 people have been killed in Syria since the country's war began with anti-government protests in March 2011.