The first official criticism came from another official, Nurettin Canikli, who is not usually a front-line spokesman on government policy.

“We cannot accept the presence of terrorist organizations that would threaten the future of the Turkish state,” Mr. Canikli, a deputy prime minister, said in an interview with the private broadcaster A Haber. “We hope the U.S. administration will put a stop to this wrong and turn back from it. Such a policy will not be beneficial; you can’t be in the same sack as terrorist organizations.”

Analysts said there were several reasons the Turkish government might play down the event: It could be looking for concessions from the United States to make up for the decision, or it could be trying to reassure its supporters or to de-emphasize the embarrassment that came from the decision being announced just as Turkish officials were arriving in Washington to lobby against it.

For their part, the Syrian Kurds expressed gratitude over the American move.

“It is a historical decision that came after years of trust and coordination between the Kurdish units and our partners in the coalition,” said Shervan Darweesh, a Syrian Kurdish official and spokesman for the Syrian Democratic Forces, the umbrella group of Arab and Kurdish fighters in Syria battling the Islamic State, also known as ISIS. “Now the fight against ISIS will be more effective and swift.”

Asked about the Turkish complaints, Defense Secretary Jim Mattis played down the disagreement.

“We’ll work out any of the concerns,” Mr. Mattis told reporters in Vilnius, Lithuania, where he was meeting with other NATO defense ministers. “I’m not concerned at all about the NATO alliance and the relations between our nations. It’s not always tidy, but we work out the issues.”

American officials said that much of the weapons and equipment that was to be provided to the Syrian Kurds was already in Syria and could be distributed very soon.

“We have a certain amount of supply in the country already,” Col. John Dorrian, a spokesman for the American-led task force that is fighting the Islamic State in Iraq and Syria, said in a briefing for Pentagon reporters. “Some of that may be distributed very quickly.”