The offensive against the towns of Marea and Azaz threatens to overrun the last swathe of territory in the east of Aleppo province held by non-jihadist rebels and bring IS to the doorstep of the Kurds' Afrin enclave.
At least 29 civilians have been killed since IS launched the assault early on Friday, the Syrian Observatory for Human Rights said.
It came as the jihadists were under attack by the Kurdish-led alliance in Raqa province further east and by the army and allied militia around Fallujah in neighbouring Iraq.
"The displaced arrived last night in areas in the west and north of Aleppo province under the control of the Syrian Democratic Forces," Observatory chief Rami Abdel Rahman said.
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The SDF is an alliance of Kurdish and Arab fighters that Washington regards as the most effective force on the ground in Syria against the jihadists of IS.
Washington's support for the alliance, which is dominated by the Kurdish People's Protection Units (YPG), has severely strained relations with NATO ally Ankara which regards it as a terror group.
IS launched its offensive against the rebel-held territory that separates it from the Kurds in Afrin on Friday.
Heavy fighting raged early today on the outskirts of Marea and around two villages on the supply route to the town of Azaz on the Turkish border to the northeast.
The jihadists managed to cut the key supply line in a surprise assault early on Friday.
The United Nations has expressed concern for some 165,000 civilians who have been trapped by the fighting between Azaz and the closed Turkish border.