Arab-Kurd forces pressed the battle to expel "Islamic State of Iraq and Syria" (ISIS) elements from the last pocket of land under their control in eastern Syria on Tuesday (February 12th) after hundreds fled the holdout overnight, AFP reported.

After a pause of more than a week to allow out civilians, the Syrian Democratic Forces (SDF) declared a last push to retake the "al-Baghouz pocket" from the extremists on Saturday.

Aided by the warplanes and artillery of the international coalition, the alliance has made way into a patch of four square kilometres.

SDF spokesman Mustafa Bali said heavy clashes were ongoing on Tuesday, after hundreds fled the battle zone overnight.

"A group of 600 civilians escaped from al-Baghouz at one in the morning and they are being searched now," he said.

The Syrian Observatory for Human Rights said the new arrivals included women and children from France and Germany.

"Most of those who got out are foreigners," Observatory chief Rami Abdel Rahman said.

"Heavy clashes are ongoing to pressure ISIS into surrendering," he said.

The Observatory said 12 SDF fighters and 19 extremists were killed in the fighting on Monday.

Coalition spokesman Sean Ryan said the SDF were facing a fierce fightback.

"The progress is slow and methodical as the enemy is fully entrenched and ISIS fighters continue to conduct counter attacks," he said.

"The coalition continues to strike at ISIS targets whenever available."