White House spokesman Josh Earnest said failure to finalize an agreement within the coming weeks "would prevent the United States and our allies from being able to plan for a post-2014 presence" in Afghanistan.
The U.S.-led war in Afghanistan is due to formally conclude at the end of next year. The security agreement under discussion would govern the relationship between the two countries after that point and could clear the way for the U.S. to leave thousands of troops in Afghanistan for training and counterterrorism purposes.
Karzai and Secretary of State John Kerry agreed to a framework for the pact on Wednesday. Following that agreement, President Barack Obama sent Karzai a letter to assure him the U.S. would continue to respect "Afghan sovereignty" under a new security agreement.
Obama also promised the U.S. military will not conduct raids on Afghan homes except under "extraordinary circumstances" involving urgent risks to U.S. nationals. The raids have been a particularly sensitive issue to the Afghans.
The security agreement is far from complete. The document now goes to the Loya Jirga, a 2,500-member council of elders that has the right to revise or reject any clause of the draft agreement.
Karzai's abrupt decision to defer signing the agreement until after the April 5 elections came even as he said he supported the Bilateral Security Agreement in a speech to the Loya Jirga.
Such a development could be a deal-breaker for the U.S. In his letter to Karzai, Obama wrote, "We look forward to completing this agreement promptly."
On the U.S. side, only the Obama administration needs to approve the agreement, but it could reject changes made by Afghan officials. If it does, that leaves open the option for the U.S. to pull all troops out of Afghanistan.
The agreement would give the U.S. a legal basis for having forces in Afghanistan after 2014 and also would allow it to use bases across the country.
Obama noted Karzai's concerns about Afghans' safety and privacy. "Over time, and especially in the recent past, we have redoubled our efforts to ensure that Afghan homes are respected by our forces and that our operations are conducted consistent with your law," he wrote. "We will continue to make every effort to respect the sanctity and dignity of Afghans in their homes and in their daily lives, just as we do for our own citizens."
The agreement set to remain in force until the end of 2024 and beyond, unless terminated by mutual agreement or by either party with two years' written notice.
While the agreement allows for a decade-long, if not longer, presence for U.S. troops, they may not be there over that period. The Obama administration has yet to specify how long U.S. troops might actually remain in Afghanistan to complete their training and support mission, and the agreement extends far past Obama's tenure as president.
U.S. officials have not yet disclosed the number of U.S. troops they want to keep in Afghanistan after 2014. U.S. officials have said the U.S. and NATO could keep between 8,000 and 12,000 troops there. Of those, the U.S. is expected to provide no more than 8,000.
Kerry said that Wednesday that whatever the number, the role of the U.S. military would be "limited."
"It is entirely train, equip and assist. There is no combat role for United States forces, and the bilateral security agreement is a way to try to clarify for Afghans and for United States military forces exactly what the rules are with respect to that ongoing relationship," he said.
Associated Press writers Deb Riechmann, Bradley Klapper and Lolita C. Baldor in Washington and Patrick Quinn and Amir Shah in Kabul, Afghanistan, contributed to this report.