In New York, the possibility of the holiday falling on Sept. 11 has intensified security concerns and fears already reverberating throughout the Muslim community after the killings of an imam and his assistant in Queens this month. For some, it also resurfaces memories of the backlash and the police surveillance directed at Muslims in the years after the attacks.

“Our community is like, ‘What are we supposed to do?’” Linda Sarsour, the executive director of the Arab American Association of New York, said. She said she had sat through extensive meetings with other leaders grappling with the possibility and how best to prepare for it.

“I should not have to think about that,” Ms. Sarsour said. “What am I supposed to tell my kids?”

Eid al-Adha honors the willingness of Ibrahim, or Abraham, to sacrifice his son Ishmael as an act of submission to God’s command. The holy day can also serve as an opportunity to honor the sacrifice of those who were killed on Sept. 11, 2001, said Abdul Bhuiyan, the secretary-general of the Majlis Ashura, the Islamic Leadership Council of New York.

“It’s a day of remembrance and observance,” Mr. Bhuiyan said.

The likelihood of this year’s Eid al-Adha landing on Sept. 11 is still unclear. Every year, the holiday takes place 10 days after the sighting of a new moon at the start of the month of Dhu al-Hijjah, according to the Islamic calendar. Exactly when the month begins depends on when a new moon is spotted, and the month is expected to start this year on Sept. 1 or 2.

In the past, another major Muslim holiday, Eid al-Fitr, has fallen near Sept. 11, but neither holiday has yet to actually coincide with the date.