ISTANBUL — Yazidi leaders and emergency relief officials on Thursday strongly disputed American claims that the siege of Mount Sinjar in northern Iraq had been broken and that the crisis was effectively over, saying that tens of thousands of Yazidis remained on the mountain in desperate conditions.

On Wednesday, the United States military said that a small team of 18 Marines and Special Operations soldiers had completed an assessment of conditions on Mount Sinjar and found that most of the Yazidis, a small Iraqi religious minority, had succeeded in escaping, and the numbers remaining were in the low thousands.

American officials said that the assessment meant American airstrikes and humanitarian airdrops, along with efforts by Kurdish pesh merga militiamen, were working and “an evacuation mission is far less likely,” in the words of the Pentagon spokesman, Rear Adm. John Kirby, on Wednesday.

Speaking from her hospital bed here, Vian Dakhil, an Iraqi member of Parliament and a Yazidi leader who was injured in the crash of a helicopter delivering aid to the mountain on Tuesday, said she was aware of the American claims and had discussed them with Yazidi leaders still in the area.