As the top American diplomat in Kabul, General Eikenberry has had nearly daily exposure to President Hamid Karzai, most recently during 20 hours of negotiations, along with Senator John Kerry, to persuade him to accept the results of an election investigation that required a second round of voting. These encounters, officials said, have left him pessimistic that Mr. Karzai will seize the challenge of creating a viable, stand-alone Afghan army.

Image Karl W. Eikenberry, a retired lieutenant general, has been the United States ambassador to Afghanistan since April. Credit... Syed Jan/European Pressphoto Agency

“No one would dispute that putting in troops will improve security,” an official familiar with General Eikenberry’s views said. “The question is, what will Afghans do? Will the Afghan government embrace the mission of training and leading combat operations? The answer is, we don’t know.”

It was not clear if the White House asked General Eikenberry to submit his comments, or if he did so on his own. But some senior officials who remain skeptical of the buildup seemed pleased that his perspective had entered the public debate, which has been dominated for two months by the leaked assessment of General McChrystal.

The behind-the-scenes tug-of-war over policy has become increasingly bitter. Last Sunday, a few days after General Eikenberry sent his cable to the State Department, top military and civilian officials gathered for a regularly scheduled meeting at the embassy, where General McChrystal pointedly addressed many of the issues in the Eikenberry memo.

General McChrystal did not refer to the cable directly, but specifically challenged General Eikenberry’s conclusions, according to one official familiar with the meeting. General McChrystal, he said, said that no alternatives had been offered besides “the helicopter on the roof of the embassy,” a reference to the hasty American withdrawal from Saigon in 1975.

After the meeting, General McChrystal and General Eikenberry had a private conference. It is unclear what was said at the meeting, but American officials said that the next day General Eikenberry sent another cable softening his stance about the impact of a troop increase in Afghanistan. A spokesman for General Eikenberry declined to comment.

As Mr. Obama left Thursday for a weeklong trip to Asia, he took his Afghanistan review with him. The president asked his military and civilian advisers not to present entirely new options, administration officials said, but rather to help choose from what he believes are the most promising elements. The discussions are not fixed on troop numbers alone, the officials said, but on underlying strategy and performance measures.