Senate Majority Leader Harry Reid said little as federal agents seized and then released cattle last week from the Bundy ranch, but there is little doubt that the highly charged episode was threatening to become a political headache for the Nevada Democrat.

The Bureau of Land Management is headed by former longtime Reid aide Neil Kornze, who was confirmed by the Senate as BLM director on Tuesday, just as federal authorities descended on the cattle ranch outside Mesquite, Nev.

Mr. Kornze issued a statement Saturday saying that the bureau would return the cattle and withdraw its agents from the ranch as a result of safety concerns after clashes between law enforcement and the Bundy family’s growing legion of supporters.

“Based on information about conditions on the ground, and in consultation with law enforcement, we have made a decision to conclude the cattle gather because of our serious concern about the safety of employees and members of the public,” Mr. Kornze said.

“We ask that all parties in the area remain peaceful and law-abiding as the Bureau of Land Management and National Park Service work to end the operation in an orderly manner,” he said.

Speculation spiked in recent days over Mr. Reid’s connection to the BLM episode, in which federal contractors seized about 400 head of cattle from 68-year-old rancher Cliven Bundy over his refusal to pay an estimated $1 million in grazing fees over 20 years.

“It was likely pressure from upstairs, rather than weapons from the field, that changed his mind on the matter,” the liberal group Americans Against the Tea Party said in an online post. “Fact is, Harry Reid probably didn’t want his name attached to the biggest civilian massacre in U.S. history right before election season.”

The Las Vegas Review-Journal, Nevada’s largest newspaper, criticized the BLM’s handling of the situation in a Friday editorial, saying the “federal government is all about intimidation and overreach.”

The grazing dispute was escalating quickly. Law enforcement reportedly used a stun gun twice on Mr. Bundy’s son Ammon during confrontations, and hundreds of supporters were driving in from out of state to demonstrate against the cattle confiscation.

Cliven Bundy has argued that his family’s cattle have grazed on the land for more than 100 years, before the BLM was founded and before a federal decision was issued to restrict grazing to protect the desert tortoise. He also has said any fees would be due to local government, not federal agencies.

“The people have the power when they unite,” Ammon Bundy told reporters last week, the Review-Journal reported. “The war has just begun.”

Gov. Brian Sandoval, a Republican, criticized the BLM’s cordoning of “free-speech areas” near the ranch and warned the agency to “be mindful of its conduct.”

“The safety of all individuals involved in this matter has been my highest priority,” Mr. Sandoval said in a Saturday statement. “Given the circumstances, today’s outcome is the best we could have hoped for. I appreciate that the Department of the Interior and the BLM were willing to listen to the concerns of the people of Nevada.”

On Sunday, BLM spokesman Craig Leff told The Associated Press that “the door isn’t closed” to an administrative or judicial resolution with the Bundys.

Mr. Kornze, 35, worked as a senior policy adviser on land-use issues in Mr. Reid’s office from 2003 to 2011 before joining the BLM. He was confirmed by the Senate on a 71-28 vote after serving as the agency’s principal deputy director, even though Republicans had qualms about his lack of experience compared with past BLM directors.

During the confirmation hearing Dec. 17, Mr. Reid called his former aide “just perfect for the job,” even as Republicans noted that previous BLM directors Bob Abbey and Jim Caswell were career federal land managers each with more than 30 years’ experience.

“I remain concerned you lack the experience required for the position of BLM director,” Sen. John Barrasso, Wyoming Republican, told Mr. Kornze at the hearing, according to the Review-Journal.

Mr. Reid made no public statement after Mr. Kornze announced the BLM’s decision.

Sen. Dean Heller, Nevada Republican, urged those who had gathered in support of the Bundy family to return home.

“The dispute is over, the BLM is leaving, but emotions and tensions are still near the boiling point, and we desperately need a peaceful conclusion to this conflict,” Mr. Heller said in a Saturday statement. “I urge all the people involved to please return to your homes and allow the BLM officers to collect their equipment and depart without interference.”

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