Much of that hinges on the bilateral security agreement that Afghan President Hamid Karzai helped forge but then refused to sign.
The U.S. wants the deal to be signed by Dec. 31 because it needs time to prepare to keep thousands of U.S. troops in the country for up to a decade. NATO allies also have said they won't stay if the Americans pull out.
The agreement aims to help train and develop the Afghan National Security Forces, and allow for a smaller counterterrorism force to go after stubborn remnants of al-Qaida and other groups.
The 350,000-strong Afghan forces were holding their ground, Dempsey said, but still need help.
Without a foreign presence, "the development of the security forces will be impeded, will be slowed, and in some parts of the country I suspect could be reversed," Dempsey said.
After a year of often-turbulent negotiations, a deal was struck on the agreement last month and Karzai presented it to a national assembly known as a Loya Jirga for approval. The assembly not only endorsed the deal but demanded that Karzai sign it by the end of this month.
Karzai says he wants his successor to sign it after the April 5 elections but said he would consider signing it himself if the U.S. adds new conditions, including ending airstrikes and raids on Afghan homes, and doing more to help broker peace with the Taliban.
Dempsey said he considered the text a done deal.
"It's not our intention to reopen the text and to renegotiate that which had been already discussed," he said.
Karzai has also lashed out at the United States, accusing it of making threats. In an interview published Tuesday by the French daily Le Monde, Karzai said the U.S. was acting like a colonial power.
Dempsey retorted: "It's not a threat. I just simply think that in any negotiation you reach a point when you've made the requirements known. And militarily, by the way, those requirements are actually quite clear."
Dempsey, who was here for a quick visit with U.S. troops ahead of the holidays, said he has not yet started making plans for a full withdrawal of all U.S. troops at the end of 2014, when a NATO mandate ends and all foreign combat forces leave the country.
"First of all I am still not planning for a zero option, although I do consider it to be an unfortunate possibility given the current impasse at achieving the bilateral security agreement," Dempsey said. "So we are not planning a zero option although we clearly understand it could be a possibility."
Allies such as Germany also want the agreement signed and have said they will not stay without the United States.
German Defense Minister Thomas de Maiziere, who arrived in Afghanistan Wednesday for a troop visit in Mazar-i-Sharif, said it was important for Karzai to sign as soon as possible to give the international contingent time to prepare, Germany's dpa news agency reported.
"I don't want to give a timeframe at this juncture when we've past the point logistically when it becomes impossible that wouldn't be tactically smart," he said, but waiting until after elections was "certainly too late."
Germany has 3,300 forces here and has pledged about 800 to remain after 2014. The U.S. has 46,000 troops in Afghanistan and its allies have another 26,000, down from nearly 150,000 two years ago.
Dempsey agreed that delays would affect the coalition.
"I hope it's resonating, that we probably are a little more agile than our NATO partners who have their own political systems, their own dynamics, their own resource-budget cycles, and I think that the real risk in delaying is that we'll begin to affect the coalition," he said.
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