The draft agreement has provoked controversy in Afghanistan where there has been strong opposition to proposals that American troops be granted immunity for crimes committed in Afghanistan.
The Afghan Government has also demanded an end to US "night raids" which it calls an invasion of privacy.
In his letter to Karzai, President Obama reassured him that Afghan homes would be respected and that night raids would be carried out only in "extraordinary circumstances" where there was a threat to US nationals.
"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.
"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," he wrote. "We look forward to completing this agreement promptly," he added.
Earlier, Secretary of State John Kerry had said the language of the agreement had been agreed and that it was now simply a matter for the Loya Jirga to decide.
The jirga is widely regarded as a "rubber stamp" body of elders selected by officials.
But the surprise opposition to the prompt agreement the US is seeking came from Karzai himself. He told the delegates that even if they accept the proposed agreement it should not be ratified until his successor is elected in April 2014.
"If you accept it and Parliament passes it, the agreement should be signed when the election is conducted ..," he said.
His deferral was based on the fact that neither he nor Washington trust one another, he said.
"It all turns to trust, and between me and America there is not very good trust. I don't trust them and they don't trust me, the last 10 years has shown this to me.
"I have had fights with them and they have had propaganda against me," he told the delegates.
Karzai said the delay would give the Americans time to reassure Afghanistan it was committed to its security.
"We want the security agreement with the condition of peace, it must bring peace to the country, I know that America can bring peace to Afghanistan if they truly want," he said.
"I have told the American leaders from the beginning that I can not talk or decide the legal immunity issue with you, that can be decided by our tribal leaders and academics in the Loya Jirga," he added.
The White House responded, saying it wanted a deal approved and signed by the end of the year.