The assault by the Syrian Democratic Forces (SDF) adds to the pressure on IS as it faces another offensive by Russian-backed regime troops in its bastion province of Raqa and in Iraq.
Supported by air strikes by the US-led coalition, the SDF alliance of Kurdish and Arab militias has made steady gains since launching the operation against Manbij last week.
The Britain-based Syrian Observatory for Human Rights monitoring group said Sunday the SDF was "now within about five kilometres" of Manbij.
The town is on a route connecting Raqa to the Turkish border, a vital conduit for supplies and foreign fighters.
US Central Command spokesman Colonel Patrick Ryder said Saturday SDF fighters had seized more than 100 square kilometres (40 square miles) of territory during the advance.
More than 55 air strikes have been carried out since the start of the offensive meant to hamper IS's ability "to move fighters, weapons, finances (and) supplies into and out of Syria and Iraq", he said.
A top SDF commander known as Abu Layla has died of wounds sustained on Friday in the battle for Manbij, the Observatory said.
Brett McGurk, US President Barack Obama's special envoy to the international coalition fighting IS, tweeted his "prayers" for Abu Layla who he said died in the operation "to liberate his hometown" Manbij.
Some 3,000 Arab fighters were taking part, backed by around 500 Kurdish militia members, while US special forces were working "at the command and control level" in the operation, he added.
- Yazidi captives freed -
In the village of Halula just east of Manbij, an AFP correspondent saw several US soldiers in jeeps as they assisted SDF fighters.
Washington has said US forces are advising the SDF on the ground but not taking direct part in combat.
In Halula, the AFP reporter saw dozens of civilians who had fled areas around Manbij, including many children, most with few belongings.
"They lived near us and we had to do what they said or they would kill our children or take our homes," mother of nine Jawaher said of IS.
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The United Nations says that at least 20,000 civilians have fled the fighting around Manbij.
At least 74 people have died in fighting since the offensive began last Monday, including 32 civilians mainly killed in coalition air strikes, said the Observatory.
Thirty jihadists were also killed along with 12 SDF fighters, said the monitor which relies on sources on the ground for its reports.
After taking the village of Khirbet al-Rus, southeast of Manbij, the SDF rescued six women and 16 children, all of them Yazidis who were being held captive by IS, it added.
IS abducted hundreds of Yazidis in mid-2014 as it carried out a brutal campaign of massacres, enslavement and rape against the minority.
- Regime raids rock Aleppo -
On Saturday, forces loyal to Syrian President Bashar al-Assad thrust into Raqa with Russian air support.
They pushed into the province from the southwest, moving to within 40 kilometres (25 miles) of the Euphrates Valley town of Tabqa, site of the country's biggest dam.
Since starting with a 2011 crackdown on anti-government protests, Syria's conflict has evolved into a complex, multi-front civil war that has left more than 280,000 dead and forced millions from their homes.
IS emerged from the chaos of the war in mid-2014, seizing control of large parts of Syria and neighbouring Iraq, declaring a fundamentalist Islamic "caliphate" and committing widespread atrocities.
Iraqi forces have also been steadily regaining ground against the jihadists, and late last month began a major offensive to retake the city of Fallujah, just 50 kilometres (30 miles) west of Baghdad.
Diplomatic efforts to get Syria's regime and non-jihadist rebels to move towards peace have been thwarted by a lack of trust and continued fighting, especially around second city Aleppo, which is divided between government and rebel control.
Dozens of regime strikes on rebel-held districts of Aleppo on Sunday killed at least 32 civilians, the Observatory said. Eight others died in rebel rocket attacks on regime-held neighbourhoods.
The violence also left more than 200 people wounded on both sides, the monitor said.
The rebel-held neighbourhood of Qaterji was devastated by a crude barrel bomb attack. An AFP journalist saw a street strewn with rubble as residents scrambled for safety and a rescuer rushed a bloodied child into an ambulance.