But, Ms. Sarsour said Ms. Siemionko refused to cooperate with the Women’s March group and that they were only trying to make the Alliance more inclusive to the city’s immigrant and minority communities.

“It’s not representative of the larger city,” Ms. Sarsour said in an interview. She instead asked for help from the New York Immigration Coalition, which oversees more than 200 community immigrant groups and of which she is a former board member. The coalition provided the money, equipment and staff for the rally.

In January, the Immigration Coalition also urged the Alliance to merge marches. By then, Ms. Siemionko said, it was too late.

“Nobody who holds a counter women’s march supports women’s rights,” she said. “There’s no justification for that behavior. None.”

[Read more about the accusations that have roiled the national women’s march movement.]

How are New York City’s Jewish leaders responding?

New York’s Jewish leaders, in particular, are conflicted because of the Women’s March NYC’s connections to the organization’s leaders in Washington. Ms. Sarsour’s resolute position defending the Boycott, Divestment and Sanctions movement in protest against Israel’s occupation of Palestine has proved problematic for some.

But her co-leader, Tamika Mallory, helped push the divide as a result of her public support of Louis Farrakhan, the leader of the Nation of Islam, who has called Jews “termites.” Ms. Mallory has condemned bigotry and anti-Semitism but has not condemned Mr. Farrakhan personally.

“If you are sympathetic to those who are prejudiced against Jews, we cannot stand with you,” Rabbi Ammiel Hirsch said in a sermon on Friday at Stephen Wise Free Synagogue on the Upper West Side. The synagogue was disassociating from the Women’s March group and any events affiliated with it; on Thursday, it will hold a panel discussion sponsored by Zioness, a women’s organization.