Under pressure from political parties wanting a diminishing American role, Mr. Maliki began demanding something in the agreement that would make it clear that American troops were on the way out. Iraq’s statement on Friday, reflecting those internal sensitivities, referred more specifically than the American version to “a time frame for the complete transfer of the security responsibilities to the hands of the Iraqi security as preface to decrease the number of the American forces and withdraw them later from Iraq.”

In Baghdad, a member of Mr. Maliki’s Dawa Party, Ali al-Adeeb, said the withdrawal of American and other foreign forces was fundamental to an accord. “The Iraqi government considers the determination of a specific date for the withdrawal of foreign forces an important issue to deal with,” he said. “I don’t know what the American side thinks, but we consider it the core of the subject.”

Mr. Adeeb suggested that a final agreement was not imminent, but White House aides said they were confident one would be reached by the end of the month. “We’re converging on an agreement,” an administration official said, noting that negotiators continued to hammer out provisions involving security matters. Those include command of military operations, legal immunities for civilian contractors and the authority to detain prisoners.

On the prospect of dates for American withdrawals, Mr. Johndroe, the White House spokesman, said that the agreement would not prescribe American troop levels over time, but rather reflect a transition to Iraqi command. “The agreement will look at goal dates for transition of responsibilities and missions,” Mr. Johndroe said in an e-mail message. “The focus is on the Iraqi assumption of missions, not on what troop levels will be.”

The agreement that American and Iraqi negotiators are now completing is more modest than the long-term strategic pact that Mr. Bush and Mr. Maliki pledged last November to negotiate to replace the United Nations mandate at the end of this year.

The administration dropped a promise in that initial agreement to provide long-term security for Iraq, something that would require a treaty and Congressional approval. It has also backed off other demands for sweeping powers to continue military operations there indefinitely.

The negotiations have been bogged down by issues involving the laws governing American troops, diplomats and civilian contractors, as well as details like customs duties and drivers’ licenses for American soldiers.