It added that Rice told Karzai that a signed agreement is necessary to plan for thousands of troops to stay in the country to train and mentor Afghan security forces to face the Taliban.
"President Karzai outlined new conditions for signing the agreement and indicated he is not prepared to sign the BSA promptly," the White House said. "Without a prompt signature, the U.S. would have no choice but to initiate planning for a post-2014 future in which there would be no U.S. or NATO troop presence in Afghanistan," she told the Afghan president.
Karzai announced his decision at a gathering of 2,500 tribal elders and regional leaders known as a Loya Jirga, even though the council not only overwhelmingly approved the deal after a four-day meeting but urged him to sign it by Dec. 31.
Washington has asked him to change his mind. But the mercurial Karzai, in the meeting with Rice, says he laid out a series of new demands albeit ones mostly involving steps the U.S. has already said it would take.
One new demand was that the United States should address a suggestion by the Loya Jirga that all Afghan prisoners be released from Guantanamo Bay, Cuba.
According to the statement, Karzai "said the United States of America should respond to the suggestion mentioned in the resolution of the Loya Jirga to free all the afghan prisoners in Guantanamo."
There are nearly 20 Afghans currently being held at the American facility in Cuba.
Karzai's office said that in the meeting with Rice, he also asked for further assurances from the United States that its forces will not raid Afghan homes and that America express a sincere commitment to help start stalled peace talks with the Taliban. He also reiterated his demand that the United States commit to holding free and transparent elections on April 5.
The statement further added that Karzai asked Rice to convey his concerns about the raids and peace talks to President Barack Obama so that he can "give assurances regarding the issues to the Afghan people."
Obama has already addressed the issue of raids in a letter to Karzai last week that was read to the assembly.
In it, Obama assured Karzai that under the agreement, the U.S. will continue to respect "Afghan sovereignty." He also said the U.S. military will not conduct raids on homes except under "extraordinary circumstances" involving urgent risks to U.S. nationals.
The US has repeatedly urged Karzai to sign a deal that would allow about 8,000 American troops to stay in the country beyond a 2014 withdrawal deadline.
The two-term Afghan leader has insisted that the winner of an April 5 election to succeed him should be the one to sign the deal. More than $8 billion in annual funds for Afghanistan's fledgling security forces and development assistance also are at stake.
Karzai may be concerned about his legacy, worried he might be seen as responsible for an agreement that some Afghans will likely see as selling out to foreign interests.
Karzai's statement said that Rice told the Afghan president that the U.S. was committed to transparent elections that will be held on time and without interference as prescribed by Afghan law.
It added that Marine Gen. Joseph Dunford, the top U.S. and coalition commander, told Karzai he had ordered his troops "to act according to the security agreement and suggestions of the consultative Loya Jirga."
But is also said Rice did not provide a commitment on the peace talks.
Karzai has blamed the United States for the collapse of talks that were to be held at a Taliban office in the Gulf State of Qatar.
The Taliban office which opened in Doha last June after talks between the United States and Qatar closed after Karzai accused the religious movement of trying to set up a government-in-exile by identifying its office as the Islamic Emirate of Afghanistan.
A furious Karzai told the Loya Jirga delegates on Sunday that Obama had promised him the Taliban would not open an embassy.
Rice met with Karzai at the end of a previously unannounced three-day trip to Afghanistan to visit U.S. troops and civilians for the Thanksgiving holidays, the White House said, adding that the meeting was at Karzai's request. Her spokesman, Patrick Ventrell, said the meeting was the last stop on her trip.
Karzai, who had convened the Loya Jirga, complicated the debate by announcing on the opening day that he wanted delegates to endorse the deal but he would not sign it.
He repeated that stance Sunday laying down a series of ill-defined conditions and promising to continue negotiations with the United States. They included demands that America ensure peace in a country that has been at war for more than 12 years and guarantee transparent elections.
Karzai, who is constitutionally barred from running in the upcoming presidential vote, also accused the United States of meddling in the 2009 elections, which were marred by fraud, and said he wanted to keep that from happening again.
Even if the president changes his mind and signs the document, it still must be approved by the Afghan parliament, then finally signed into law by Karzai.
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Associated Press Writers Jim Kuhnhenn aboard Air Force One, Nedra Pickler and Pauline Jelinek in Washington contributed.
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Follow Patrick Quinn on Twitter at www.twitter.com/PatrickAQuinn