Heavy fighting was underway near the northern city's airport where government forces retreated, highlighting the potent challenge the militants pose after their lightning capture of Kunduz.
The Taliban's occupation -- now in its third day -- raises troubling questions about the capabilities of Afghan forces as they battle the militants largely on their own after NATO's combat mission ended last December.
The Afghan army was supposed to be bolstered by its own reinforcements for the campaign to retake Kunduz, but attacks on convoys making their way to the city meant that back-up troops were only trickling in.
NATO said the foreign special forces have reached Kunduz and US forces have conducted three air strikes around the city since Tuesday to support the Afghan troops.
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The forces are comprised of US, British and German troops, a Western military source told AFP on condition of anonymity, without specifying the number.
The Afghan spy agency said the overnight strikes killed Mawlawi Salam, the Taliban's "shadow governor" for the province, along with his deputy and 15 other fighters.
The Afghan security official said the militants had slowly infiltrated Kunduz during the recent Eid festival, launching a Trojan horse attack that enabled them to capture it within hours.
Pentagon press secretary Peter Cook said the fall of the city on Monday -- achieved by a militant force significantly smaller than the army contingent -- was "obviously" a setback but the US believed Afghan authorities would be able to regain control.