The Northern Alliance says Taliban commanders have agreed to let their troops into Kunduz.
Alliance fighters, apparently unaware of the breakthrough, launched an offensive outside Kunduz just as details of the agreement emerged.
Fighters attacked Taliban positions east of the city with rocket launchers, artillery and tanks.
Pentagon spokesman Marine Lt Col Dave LaPan said 75 US aircraft struck Taliban military forces, tunnels and caves over the previous 24 hours, concentrating on the Taliban stronghold of Kandahar in the south and the Jalalabad area in the east.
The alliance says that under the purported deal for the surrender of Kunduz, reached during negotiations in the alliance-held city of Mazar-e-Sharif, Afghan fighters would be allowed to leave the city.
Officials say that Arabs, Pakistanis and other foreign fighters loyal to Osama bin Laden will be placed in camps until the alliance and the US-led coalition decide what to do with them.
The US has insisted that suspected al-Qaida members should not be allowed to go free as part of any deal.
Alliance spokesman Ashraf Nadeem says the alliance will send 5,000 fighters to Kunduz "possibly Saturday" to oversee the Taliban surrender.
Both sides are to meet in Mazar-e-Sharif to finalise details.
Alliance fighters said they feared the foreign fighters - thought to number up to 3,000 - might try to break out of the city and escape to Uzbekistan or Pakistan rather than accept surrender.