The Syrian Democratic Forces (SDF) Kurdish-led alliance supported by a US-led coalition is battling to expel the jihadists from a pocket in the eastern province of Deir Ezzor on the Iraqi border.
The Britain-based Syrian Observatory for Human Rights monitor said the jihadists launched "three separate assaults" on Saturday.
The monitor said the counter-attacks targeted the villages of Al-Bahra and Gharanij and an area close to the Al-Tanak oilfield, which is commercially active but is also an SDF military position.
SDF spokesman Mustefa Bali confirmed "a series of attacks" led by IS in these three locations and said fighting had taken place all day, with the Kurdish-led ground forces receiving coalition air support.
The fighting on Saturday alone killed 29 SDF fighters, taking its total losses over the last two days to at least 47, said Observatory head Rami Abdel Rahman.
Thirty-nine IS jihadists have been killed -- some in the ground clashes, others in air strikes -- over the same period, the Observatory said.
- 'A broad attack' -
IS confirmed in a statement on Telegram that it had launched attacks near Al-Bahra and Gharanij.
Earlier, the Observatory said IS had broken out of its holdout on Friday to attack Al-Bahra, where SDF fighters and coalition advisers are based.
"IS launched a broad attack on the village of Al-Bahra next to its holdout, taking advantage of the fog," Abdel Rahman said.
The monitor said coalition raids have also killed 17 civilians, including five children, in the IS-held pocket since Friday.
Coalition spokesman Sean Ryan said he had not received any reports of civilian casualties, and insisted air strikes had been "very limited due to the weather".
Deir Ezzor activist Omar Abu Leila said the attack on Al-Bahra was "very scary" and that IS fighters were able to move quickly "taking advantage of the fog".
- 'Probable chlorine attack' -
Meanwhile Syrian regime shelling killed nine civilians including seven children Saturday in a planned buffer zone around the country's last major rebel bastion, the Observatory said.
A teacher and four schoolchildren were among the victims after the shelling hit near a school in the northwestern province of Idlib, said Abdel Rahman.
Later in the evening, in neighbouring Aleppo which is under Syrian regime control, official media accused the rebels of launching an attack with "toxic gas".
Regional head of health services, Ziad Hajj Taha, said it was a "probable" chlorine attack.
It is not the first time such accusations have been levelled against the rebels in Aleppo. On other occasions the Syrian regime has been accused of using chemical weapons against rebel strongholds, which it has always denied.
The anti-IS alliance has repeatedly denied previous reports of civilians killed in its air strikes, and said it does its utmost to avoid hitting non-combatants.
IS overran large swathes of Syria and neighbouring Iraq in 2014, proclaiming a "caliphate" in land it controlled but has lost most of it to offensives by multiple forces in both countries.
In Syria, the jihadists are largely confined to the pocket in Deir Ezzor, but they also have a presence in the vast Badia desert that stretches across the country to the Iraqi border.
Since 2014, the US-led coalition has acknowledged direct responsibility for over 1,100 civilian deaths in Syria and Iraq, but rights groups put the number much higher.
Syria's war has killed more than 360,000 people and displaced millions since it started in 2011 with the brutal repression of anti-government protests.