The abductions came as Russian and Syrian jets pounded rebel positions in and around second city Aleppo, killing at least 20 people, the Syrian Observatory for Human Right monitor said.
The Arab-Kurdish alliance known as the Syrian Democratic Forces (SDF) expelled most of the Daesh fighters from Manbij last week, but dozens continued to put up a tough resistance.
On Friday they withdrew from a northern neighbourhood heading for the Daesh-held town of Jarabulus along the border with Turkey, taking the captives with them.
“While withdrawing from a district of Manbij, Daesh jihadists abducted around 2,000 civilians from Al Sirb neighbourhood,” said Sherfan Darwish, spokesman for the Manbij Military Council, a key component of the SDF.
“They used these civilians as human shields as they withdrew to Jarabulus, thus preventing us from targeting them,” he said, adding that women and children were among those taken.
The Britain-based Observatory, which relies on sources inside Syria to cover the war, gave a similar report, saying Daesh forced around 2,000 civilians into cars it confiscated and headed for Jarabulus.
In January, Daesh abducted more than 400 civilians, including women and children, as it overran parts of Deir Ezzor province in eastern Syria. It later released around 270 of them.
Daesh has also used civilians as human shields, booby-trapped cars and carried out suicide bombings to slow advances by their opponents and avoid coming under attack.
Thousands of civilians were held captive by the group in Fallujah which Iraqi forces recaptured in June after a four-week offensive.
SDF forces captured Manbij on August 6 but continued to battle pockets of jihadists holed up in parts of the town.
Darwish said the SDF rescued 2,500 civilians who were held captive by Daesh fighters before they fled and combed Al Sirb on Friday for any remaining jihadists.
With air support from the US-led coalition, the SDF began its assault on Manbij on May 31, surging into the town itself three weeks later.
But their offensive was slowed by a massive jihadist fightback, before a major push last week saw the alliance seize 90 per cent of the town.
Tens of thousands of people lived in Manbij before the assault started in May.
The United Nations has said that more than 78,000 people have been displaced since then.
Manbij was a key transit point along IS’s supply route from the Turkish border to Raqa, the de facto capital of its self-styled Islamic “caliphate”.
The Britain-based Observatory says the battle for Manbij claimed the lives of at least 437 civilians – including 105 children – and killed 299 SDF fighters and 1,019 jihadists.
Raids on Aleppo
The Observatory said women and children were among at least 20 people killed Friday in Syrian and Russian air raids on rebel positions in Aleppo and rebel positions further north and west of the city.
Twelve were killed in Hayyan, a small town 15 kilometres north of Aleppo, it said.
An AFP correspondent in the rebel-held east of the city said several neighbourhoods were hit, adding that people had been out on the streets to stock up on supplies after weeks of shortages caused by a punishing government siege.
Syria’s state news agency SANA, quoting a military source, said the warplanes destroyed several rebel positions and vehicles and killed “dozens of terrorists”.
The Observatory said clashes raged between rebels and pro-regime forces south of Aleppo.
Friday’s raids come despite a pledge by Russia to observe a three-hour daily ceasefire in Aleppo to allow for humanitarian aid deliveries.
An estimated 1.5 million people live in the city, including about 250,000 in rebel-held districts.
Syria’s conflict erupted in March 2011 and has since killed more than 290,000 people and drawn in world powers on all sides of the war.