KABUL, Afghanistan — There was an air of expectation on both sides as the Taliban and American diplomats gathered to meet for the latest round of peace talks on Saturday.

Afghan and Western officials say that if the Taliban express willingness to finally go to the negotiating table with the Afghan government, American diplomats might be willing to play their main negotiating card: offering some sort of provisional schedule for the withdrawal of United States troops from Afghanistan.

That phase of agreement has evaded negotiators for more than nine months, through six rounds of talks in Doha, Qatar. The hardest work, however, might come only after the Taliban and Afghan officials agree to begin discussing a political settlement.

The Taliban have remained officially vague about what kind of government they envision. But some clues to how the insurgents view power and governance can be found in a constitution that the group drafted while it ruled Afghanistan but that was never ratified before the Taliban were ousted by the United States invasion in 2001.