HOORN, The Netherlands — On a wintry night in January 2005, an art thief slipped into the Westfries Museum here, the authorities believe, and hid beneath drapery on a 17th-century coffin as the doors were locked for the night.

After disabling the alarm system, the theory goes, the thief allowed at least one collaborator into the small museum, which houses works from the Dutch Golden Age. When the Westfries opened the next morning, 24 paintings worth a total of about 1.3 million euros, about $1.44 million, along with 70 pieces of antique silver, were gone, leaving only frames hanging on the gallery walls.

For a decade, the whereabouts of the stolen works remained a mystery, and the assumption was that they had disappeared into the murky world of international art theft.

Then, this summer, representatives of an ultranationalist militia in Ukraine contacted the Dutch Embassy in Kiev, saying the group had discovered the art in a villa near Donetsk that had belonged to the government of the deposed president Viktor F. Yanukovych and was prepared to return it.

“They said that as a good gesture, we want to hand over the paintings,” Ad Geerdink, the director of the Westfries Museum, which went public with the case last week in an effort to recover the works before they could be sold on the black market, said on Saturday, “but since we risked our lives to save the paintings, we expect something in return. And that something, of course, was money.”

The museum hired Arthur Brand, a Dutch art crime investigator, to go to Ukraine to negotiate with the militia, the Battalion of the Organization of Ukrainian Nationalists. “I told them to be careful,” Mr. Brand said in a telephone interview on Monday, “because, although they said they would be willing to give the work back, they were talking about a finder’s fee, and they had estimated that the work was worth 50 million. I guessed already that they’d ask for 10 percent.”

On Aug. 7, Mr. Brand said, he and representatives from the Dutch Embassy met with Borys Humeniuk, the deputy commander of the battalion, in Kiev and presented him with documentation that estimated the value of the works at 500,000, on the assumption that they were now in bad condition after almost a decade on the black market, and offered him a fee of 50,000.

After hearing that offer, Mr. Humeniuk no longer seemed so willing to return the paintings and the silver, he said.

“Borys repeated two times, ‘My soldiers will not accept this’ and he said, ‘the people who sent me will not accept 50,000,”’ Mr. Brand said. “Then the meeting was over and he said, ‘I will do my best to negotiate with my people.’ Then we waited.”

In early September, the Westfries Museum officials contacted the Ukrainian authorities, Mr. Geerdink said. Months passed without any progress in the case, he said.

During that time, Mr. Brand said, he received information that the art was being offered for sale to other parties.

“We hear from our informants that they first offered to other groups 24 paintings, and then we heard about 16, and then we heard about 12,” he said. “That was a strong indication that they were succeeding in selling at least some of the paintings. That was a strong motivation for us to go to the press.”

Mr. Geerdink said: “We felt it was now or never. If we don’t act, the work will be sold and we’ll never get it back.”

“We want potential buyers to know that it’s stolen art,” he added, “and we want to motivate the Ukrainian officials, because they say they will do something, but they never tell us what they do.”

The stolen works are by relatively unknown Dutch Golden Age painters, including Jan van Goyen, Jan Linsen and Jacob Waben. “When you look at it from an international or national perspective, the paintings weren’t Rembrandts, Jan Steen or Vermeer; they were the category below,” Mr. Geerdink said. “When you look at it on a regional or local scale, they’re invaluable, because there aren’t similar paintings. These are landscapes or cityscapes and marine paintings that are so important for the story that we as a museum tell about the Golden Age of this area.”

The money to recover the paintings was to be provided by the municipality of Hoorn, since the Westfries museum itself has an annual operating budget of just ㄠ80,000 and an annual acquisitions budget of ㄠ1,000.

Museum officials and investigators involved in the case said that the works were probably not stolen by Ukrainians — the best guess at this point is that Dutch thieves were involved — and that they have probably changed hands a number of times in the past decade.

How they ended up in Ukraine is a matter of conjecture. Mr. Geerdink said the first indication that they might be there surfaced in 2014, when a Dutch police detective discovered a color image of one of the missing art works, “Rebecca and Eliezer,” by Linsen, on a Ukrainian website.

In response to the Westfries’ effort to publicize the case, the Ukrainian national police chief, Khatia Dekanoidze, said she was waiting for an official request from the Dutch prosecutor general’s office to begin to coordinate an investigation.

“Our doors are open, we’re transparent and I hope that any kind of delegation from the state of Netherlands can arrive here,” she said in a videotaped statement on Friday.

Olexander Horin, the Ukrainian ambassador to the Netherlands, criticized the museum and the Dutch authorities for meeting with Mr. Humeniuk without first contacting Ukrainian authorities.

“We consider these talks, frankly speaking, inappropriate,” he said in a telephone interview on Monday. “This is a very sensitive issue and if you choose to go ahead and do this yourself, you have to bear the responsibility for the result. It’s like a kidnapping case, when the goals of the investigators and the parents are completely different.”

At this point, Mr. Horin said, the Ukrainian government is taking several steps, “first to locate the paintings, second to apprehend them, if these are the paintings they’re looking for, and the third and next step is the transfer of these paintings to the Dutch parties.”

Ahmed Dadou, press secretary to the Dutch minister of foreign affairs, Bert Koenders, said on Monday in a telephone interview: “We are in close contact with the Ukrainians on the proceedings in this case, and the Ukrainians have assured us that they would investigate the case.”

In the meantime, the Westfries Museum has re-hung many of the empty frames of the paintings in the museum’s upstairs galleries.

“Our fear is that maybe at this moment some of the paintings have already been sold,” Mr. Geerdink said. “We hung up the empty frames in the museum as a sign of protest and also as a sign of hope that within a year we’ll be able to recover them.”