The Syrian Democratic Forces (SDF), an Arab-Kurdish alliance supported by US-led coalition air strikes and special forces advisers, surrounded Tabqa in early April and have cut its main supply routes.
The town and a vast nearby dam are considered key prizes in the broader offensive for Raqa, the de facto Syrian capital of IS's self-proclaimed "caliphate", about 55 kilometres (34 miles) to the east.
An SDF military source said Saturday that clashes were "at their height" and that the alliance's forces were "trying to penetrate the town from the east and west".
SDF fighters are within a few hundred metres (yards) of Tabqa, said Rami Abdel Rahman, head of the Syrian Observatory for Human Rights, a British-based monitoring group.
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He said heavy clashes were under way around the two suburbs as IS attempted to counter-attack.
The SDF launched its campaign for Raqa in November and has since captured most of the surrounding province.
It has been backed by US-led coalition air strikes, along with advisers and even an American Marines artillery battery.
Tabqa sits on a key supply route into Raqa and served as an important IS command base, housing the group's main prison.
Syria's war has left more than 320,000 people dead since it began with protests in 2011 that were brutally repressed.
It has since drawn in jihadist groups as well as regional and international powers in a complex multi-sided conflict.
The fighting has caused millions to flee their homes and triggered a major humanitarian and refugee crisis.
It said the explosion took place at Rashidin, west of second city Aleppo, where buses were waiting to transport thousands of people who left Fuaa and Kafraya a day earlier.
More than 7,000 people who had been under crippling siege for more than two years left four Syrian towns on Friday under a delayed evacuation deal brokered by Iran and Qatar.
Around 5,000 people piled onto buses leaving Fuaa and Kafraya while a further 2,200 were evacuated from rebel-held Madaya and Zabadani.
An AFP correspondent in Rashidin, where 5,000 evacuees from the two government-held towns were awaiting onward transport, said the buses had yet to move 30 hours after the operation began.
Around 2,220 evacuees from Madaya and Zabadani were similarly blocked at a transit point in government-held territory, one of them told AFP by telephone.