GRAND RAPIDS, Mich. — After deliberating all week, jurors said Friday morning that they had reached a verdict on several charges in the trial of four men accused of plotting to kidnap the governor of Michigan but that they were deadlocked on other charges. The judge told them to continue deliberating to try to reach agreement on all counts.

The note from the jury on Friday was the first substantive update on the progress of deliberations since closing arguments concluded a week ago, in one of the highest-profile domestic terrorism cases in decades.

Prosecutors said the men — Brandon Caserta, Barry Croft, Adam Fox and Daniel Harris —  wanted to kidnap Gov. Gretchen Whitmer, a Democrat, at her vacation home in northern Michigan in 2020. Defense lawyers argued that there was no firm plan to abduct the governor, and that their clients had been drawn into heated political conversations by F.B.I. informants and undercover agents.

It was not clear which of the criminal counts the jurors were deadlocked on.

All four men face a kidnapping conspiracy charge that carries a potential penalty of life in prison. Mr. Croft, Mr. Fox and Mr. Harris are also accused of planning to blow up a bridge and are charged with conspiracy to use a weapon of mass destruction. Mr. Croft and Harris are also accused of illegally possessing a destructive device, and Mr. Harris is accused of illegally possessing a short-barreled rifle.

Late on Thursday, the fourth full day of deliberations, jurors asked to see an exhibit that was tied most closely to the possession of a destructive device charge. Earlier in the week, they asked about the definition of “weapon,” a word that seemed most relevant to the weapon of mass destruction and destructive device charges.

On Friday, Chief Judge Robert J. Jonker encouraged jurors to keep deliberating. But he told them that he knew they had already spent days reviewing the evidence and that they should not violate their consciences to reach unanimity.

“I know you’ve been at it a while,” Judge Jonker, of the Federal District Court for Western Michigan, told the jury of six men and six women. “It’s not as if you came to us in the first few hours and said, ‘Oh, we give up.’” He added: “Indulge me, if you would — one more effort.”

During weeks of testimony at the federal courthouse in Grand Rapids, prosecutors showed jurors inflammatory social media posts and chat messages from the defendants, and played audio secretly recorded by an F.B.I. informant. One former co-defendant who pleaded guilty testified that he had hoped to set off a chain of events that would prevent Joseph R. Biden Jr. from being elected president, and perhaps foment a civil war.

“That was the whole plan: They wanted to kick that off by kidnapping the governor,” Nils Kessler, a federal prosecutor, said during closing arguments.

The case against the four men was seen by many as a lens into an increasingly brazen, violent discourse among some far-right groups as well as the threat posed by members of the militia movement. The men charged in Michigan were arrested months before a violent right-wing mob disrupted the certification of the presidential election on Jan. 6, 2021, but scholars on domestic extremism said the openness to political violence and embrace of political conspiracy theories alleged in both cases represented a chilling pattern.

In the first months of Mr. Biden’s term, federal law enforcement stepped up efforts to combat domestic extremism, and the administration called white supremacists and militia groups a top national security threat.

In the Michigan courtroom, testimony focused narrowly on the conversations and training of the men accused of planning to kidnap the governor.

Witness after witness for the prosecution recounted regular training sessions during the summer of 2020, called “field training exercises,” where members went through shooting drills, received medical training and practiced navigation skills. Others described how some members of the group twice went to scope out Ms. Whitmer’s vacation home in northern Michigan, where prosecutors said they planned to snatch her. (On one of those trips, they had the wrong address for the house, so they just drove aimlessly down her street.)

No attack ever took place, no final date for an abduction was set, testimony showed, and the details of the alleged plan sometimes differed from witness to witness. The F.B.I. informant, Dan Chappel, said he believed the group had planned to kill Ms. Whitmer, whose handling of the Covid-19 pandemic had infuriated the men. Ty Garbin, the man who earlier pleaded guilty in the case, said he thought the group of men might abandon the governor in a boat in the middle of Lake Michigan. Another man who pleaded guilty, Kaleb Franks, said he had hoped to die in a shootout with the governor’s security detail.

“There was no plan to kidnap the governor, and there was no agreement between these four men,” Joshua Blanchard, a lawyer for Mr. Croft, said in closing arguments. He said the government tried to conjure up a conspiracy by using a network of informants and undercover agents, and that “without a plan, the snitches needed to make it look like” there was movement toward a plan.