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WASHINGTON, Oct 19 (Reuters) - Afghan President Hamid Karzai has indicated in private meetings he would be open to a run-off election but he has yet to commit to a specific timetable, Western sources said on Monday.

Karzai plans to announce on Tuesday how he intends to proceed after a U.N.-backed fraud watchdog invalidated tens of thousands of votes for him in the August presidential election, making a run-off likely.

Karzai has previously opposed a run-off against his main presidential election rival, Abdullah Abdullah, warning that could lead to ethnic violence.

U.S. Secretary of State Hillary Clinton said earlier on Monday that she was "encouraged at the direction that the situation is moving" and was "very hopeful that we will see a resolution in line with the constitutional order in the next several days."

Karzai indicated his willingness to accept a run-off in meetings this week with visiting Western officials, including U.S. Senator John Kerry, according to the sources, who spoke on condition of anonymity.

Even if Karzai publicly accepts a run-off in principle on Tuesday, Western sources said a lot of uncertainty remains.

They said the president has yet to commit to holding the vote immediately, and it that it was unclear whether the Afghan elections commission would be able to carry out the vote given the rising number of Taliban attacks against U.S. and NATO forces and their Afghan allies.

Western officials see only a short window of opportunity for holding a run-off before winter weather sets in. Unless it happens in the next several weeks, voting would have to be put off until spring, an outcome Washington sees as untenable.

"Even a little bit of foot-dragging would result in it not being feasible," one of the sources said. (Reporting by Adam Entous and Sue Pleming, Editing by Doina Chiacu)

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