* Kerry: security pact should be signed "sooner, not later"
* U.S., NATO say they would pull out without deal
* NATO chief says pullout would harm Afghan security
* Karzai loath to sign accord, has added conditions
U.S. Secretary of State John Kerry suggested on Tuesday that Afghanistan's defence minister or government, instead of a reluctant President Hamid Karzai, could sign a security pact enabling some U.S. troops to stay in the country after 2014.
An assembly of Afghan elders, the Loya Jirga, last month endorsed the security deal with the United States, but Karzai said he might not sign it until after elections next April.
The delay has irritated the United States and its allies, which want to get on with planning for the smaller, NATO-led training mission that is to stay on in Afghanistan after 2014, when most foreign troops that have been battling Taliban insurgents will have pulled out.
Kerry urged the Afghan government to sign the security deal "sooner, not later" and said this priority was backed by all NATO foreign ministers taking part in a meeting on Tuesday.
"This is not fooling around ... This is serious business," Kerry told a news conference in Brussels.
"I think it is important for the agreement to try to move forward. It doesn't have to be pres(ident)," he said, not finishing the word. "You know, his minister of defence (Bismullah Khan Mohammadi) can sign it, the government can sign it, somebody can accept responsibility for this.
"But I think it is important, for planning purposes, for people who have been extraordinarily patient, who are trying to allocate major amounts of money to sustaining this effort in Afghanistan, to have knowledge of where they are going."
Kerry said he had personally negotiated the agreement with Karzai and did not believe in unilateral renegotiation.
After the sacrifices made by U.S. troops and the American people to contribute to Afghanistan's future, Kerry said he didn't think President Barack Obama appreciated that the pact was "being left in doubt at this critical moment."
Other NATO leaders also urged Karzai to swiftly sign the security pact, saying failure to do so could jeopardise Afghan security and up to $8 billion a year in foreign aid.
U.S. and NATO officials have warned that if Karzai does not sign the security deal with the United States promptly, both Washington and the alliance would have to withdraw all troops from Afghanistan by the end of 2014 and abandon plans to leave behind a training force of around 8,000-12,000 soldiers.
The NATO-led force now has 84,000 troops in Afghanistan, the majority American. NATO is winding down combat operations, handing responsibility for fighting the Taliban to the Afghans, before most foreign combat forces pull out by the end of 2014.
"My concern is that if we are not able to deploy a training mission to Afghanistan, it may have a negative impact on the security situation in Afghanistan and furthermore it may also have a negative impact on the provision of financial aid to Afghanistan," NATO Secretary-General Anders Fogh Rasmussen told reporters.
He said he looked forward to Karzai's "timely signature" of the U.S. security pact.
Although terms of the Afghan-U.S. pact were settled after a year of wrangling, Karzai has since added conditions including the release of all Afghan prisoners from Guantanamo Bay in Cuba and an end to military operations involving Afghan homes.
A senior diplomat at NATO said U.S. National Security Adviser Susan Rice had made clear on a recent visit to Kabul that Washington would begin planning a total pullout by the end of 2014 unless Karzai signed by the end of this year.
Kerry said, however, that Obama had urged Karzai to sign the pact by "a period of time" but had set no ultimatum.