"While withdrawing from a district of Manbij, Daesh (IS) 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 Syrian Observatory for Human Rights, which relies on sources inside Syria to cover the war, gave a similar report, saying IS forced around 2,000 civilians into cars it confiscated.
The jihadists, who have suffered a string of losses in Syria and Iraq, have often staged mass kidnappings when they come under pressure to relinquish territory they hold.
"Although fighting in Manbij continues, ISIL is clearly on the ropes. It has lost the centre of Manbij, it has lost control of Manbij," Pentagon deputy press secretary Gordon Trowbridge said, using another name for the group.
- 'Human shields' -
The EU denounced the use of civilians as human shields, saying in a statement that "Daesh (IS) continues to pose a threat to the people of Syria, Iraq, the region as well as to Europe and beyond".
IS has also used civilians as human shields, booby-trapped cars and carried out suicide bombings to slow advances by their opponents.
Thousands of civilians were held captive by the group in Fallujah, which Iraqi forces recaptured in June after a four-week offensive.
On Friday, the SITE intelligence Group said IS had killed five men in Iraq for smuggling people out of territory it controls.
SDF forces captured Manbij on August 6 but continued to battle pockets of jihadists in parts of the town.
Darwish said the SDF rescued 2,500 civilians who were held captive by IS 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 percent 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 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 withdrawal in Manbij came as Russian and Syrian jets pounded rebel positions in and around second city Aleppo, killing at least 20 people, the Observatory said.
The Observatory said women and children were among those killed.
Twelve people were killed in Hayyan, a small town 15 kilometres (10 miles) 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 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.
The Observatory also reported that a strike on the town of Kafr Hamra north of Aleppo hit a hospital used by rebels, killing a nurse and another employee.
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.