Ms. Merkel, who recently marked a decade in power, had come under fire from several blocs in her Christian Democratic Union for refusing to put a cap on the number of new arrivals. But at a party meeting, she deflected her opponents by promising that the number would drop and that refugees had to respect German law and customs.

On Sunday, she agreed to adapt a party resolution to reflect the concerns of the conservatives. That resolution was adopted late Monday with two votes against and a few abstentions.

The chancellor pleaded in a 73-minute speech for Germans to recognize that “it is not human masses that are coming to us, but individual human beings.” She also lauded the civic effort to welcome the refugees as “the best and most convincing answer to all those who try, with hatred and incitement in their hearts, to whip up sentiment against strangers.”

“In the 21st century,” Ms. Merkel said, “cutting oneself off is not a rational option.”

Delegates responded with a nine-minute standing ovation.

Ms. Merkel also reiterated her belief that multiculturalism “leads to parallel societies” rather than integration and is therefore “a sham.”

She first pronounced “multikulti” to be “dead” in 2010 and has cast her embrace of refugees in much more sweeping terms as a chance for Germany to change and benefit in much more lasting ways than a surface acceptance of differences while different communities live very separate lives.

Later, Interior Minister Thomas de Maizière, who has at times seemed at odds with the chancellor, underscored the party’s two-pronged approach of continuing to welcome newcomers while cutting back benefits.

The government has to find “a balance between its human duty and avoiding overreach,” he said. Refugees, he urged, should also be patient as Germany copes with so many new arrivals.