US-led coalition air strikes supporting the assault by Kurdish and Arab fighters, launched on May 31, have also left 30 civilians dead, said the Syrian Observatory for Human Rights.
The Syrian Democratic Forces have been pushing west from the Euphrates River and have nearly encircled Manbij, a key point along IS's main supply line from the Turkish border to its eastern Syrian stronghold of Raqa.
The SDF alliance has surrounded the city from the north, east and south. Early on Thursday its fighters were advancing towards the main road leading west out of Manbij, according to Observatory head Rami Abdel Rahman.
The Britain-based Observatory, which relies on a network of activists and medical sources inside Syria, said 132 IS jihadists and 21 SDF fighters had been killed since the start of the offensive.
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"Most of the Daesh fighters were killed in air raids by the international (US-led) coalition," Abdel Rahman told AFP, using an Arabic acronym for the group.
He said dozens of bodies of IS fighters had been found this morning in small villages east of Manbij.
They are among a total of 447 civilians killed in coalition raids since they began in Syria in September 2014, according to the monitor's tally.
The Observatory says it determines whether strikes are carried out by Syrian, Russian or US-led coalition aircraft based on their locations, flight patterns and the types of planes and munitions involved.
A spokesman for the US defence department said on Wednesday that the final assault on Manbij could take place within days.