The Syrian Democratic Forces (SDF) broke into Tabqa from the south last week and have steadily advanced north, cornering IS in three contiguous neighbourhoods on the bank of the Euphrates River.
The strategic town of Tabqa sits on a supply route about 55 kilometres (35 miles) west of Raqa city, the de facto capital of IS territory in Syria.
At dawn, IS fighters withdrew from the western-most district towards the other two quarters, said Rami Abdel Rahman, head of the Syrian Observatory for Human Rights.
"In the whole town, IS only holds those two neighbourhoods, known locally as the first and second quarters," he told AFP.
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Clashes and bombing raids by the US-led coalition were rocking the town on Monday morning, the Observatory reported.
The assault on Tabqa began in late March when SDF forces and their US-led coalition allies were airlifted behind IS lines.
The SDF -- composed of Arab and Kurdish fighters -- then surrounded Tabqa in early April before pushing into the town on April 24.
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.