IS swept towards the opposition strongholds of Marea and nearby Azaz in Aleppo province on Friday, forcing thousands of civilians to flee.
Rebel groups in Azaz tried to launch a counter-offensive on Tuesday but failed, said the Syrian Observatory for Human Rights.
IS blocked the attack with a suicide bomber, killing six rebel fighters, the Britain-based monitor said.
"The battles are intensifying," said Observatory head Rami Abdel Rahman.
The United Nations said it was "deeply concerned over the fate of an estimated 8,000 Syrians trapped by fighting around the towns of Marea and Sheikh Issa" following IS advances.
"An unknown number of people are also unable to flee due to fighting and the closure of the main road leading north towards the town of Azaz," it said in a statement.
It said that fighting was also "reported to be continuing near the towns of Kaljibrin and Kafr Kalbin where some 6,000 people are living.
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"Of the estimated 1,650 individuals recently displaced to informal settlements in the Yazibag area, northeast of Azaz, most have come from areas where fighting has been reported."
The Observatory said rebels continued to shell the Sheikh Maqsud neighbourhood on Tuesday.
Rebels have been shelling Sheikh Maqsud for months after an advance by Kurdish forces into rebel territory west of Marea, Abdel Rahman said.
An estimated 130 civilians have died in the shelling since February, he said.
The UN has said that the recent clashes have also trapped some 165,000 civilians between Azaz and the closed Turkish border.
Pablo Marco, the regional manager of Doctors Without Borders, said Monday tens of thousands -- many of them already displaced from other areas -- were caught less than five kilometres (three miles) from the front line with "nowhere to go".
Also in Aleppo city on Tuesday, four civilians were killed in air strikes on a car crossing the bombed-out Castello road, the civil defence rescue force told AFP.
At least 280,000 people have been killed and more than half of Syria's population have fled their homes since the conflict first erupted in 2011.