BANGKOK — A Belarusian woman and her nine companions from Russia and Belarus jailed for allegedsex-related activity in Thailand have sent a letter to the U.S. Embassy Wednesday seeking asylum in exchange for what they say is criminal evidence concerning Russians who may be linked to U.S. President Trump.

The 10 jailed people include Anastasia Vashukevich, the reported “mistress” of Russian billionaire Oleg Deripaska also known as Nastya Rybka, who figures prominently in a sensational video expose released earlier this month by Russian opposition leader Alexei Navalny and quickly suppressed by the Kremlin.

Relying heavily on Ms. Vashukevich’s writing and Instagram account, the video charged there are close personal and financial ties between Mr. Deripaska and Russian Deputy Prime Minister Sergei Prikhodkho, a close aide to Russian President Vladimir Putin.

Mr. Navalny’s video said Mr. Deripaska, who amassed a huge fortune in the metals industry, was a key link to Mr. Trump because of his relationship with former Trump campaign manager Paul Manafort.

Mr. Prikhodkho and Mr. Navalny were named in their letter, which said “U.S. relations with Russia” and “very important information for USA” were involved.

“We have photo-video-audio of crymes [sic] of Russian government. And I give them USA if you help us,” the letter said, according to Khaosod English, a Thailand-based online news service which published a photograph of the letter.

Addressed “To USA Consul,” it was written by Alexander Kirillov, a Russian also known as Alex Lesley, who was jailed along with the others. The letter did not reveal evidence or details to support their claim.

The “political asylum” request came the same day Thai Prime Minister Prayuth Chan-ocha. met in Bangkok with the visiting Russian security council secretary and former Federal Security Service director Nikolai Patrushev.

They talked about bilateral tourism and security, but it was not publicly known if they discussed the 10 jailed people.

The Russian and Belarusian tourists were arrested on Sunday in Pattaya, a beach resort on the Gulf of Thailand with a reputation for sex tourism, where they allegedly participated in illegal lessons about sex, taught by Mr. Kirillov.

Thai officials said they received complaints about the $700 weeklong class and, after raiding the meeting, arrested the 10 for visa violations and working without a permit. Foreigners working without a permit can be jailed up to five years but are usually fined and deported, which is what the group of 10 now fear.

Ms. Vashukevich calls herself Nastya Rybka on her Instagram account (@nastya_rybka.ru) where she introduces herself to more than 100,000 followers as “Deripaska’s mistress.”

In a live Instagram posting Tuesday, she claimed to be the “only witness and the missing link in the connection between Russia and the U.S. elections — the long chain of Oleg Deripaska, Prikhodko, Manafort, and Trump.”

“In exchange for help from U.S. intelligence services and a guarantee of my safety, I am prepared to provide the necessary information to America or to Europe or to the country which can buy me out of Thai prison.”

Mr. Deripaska has denied the charges and threatened to sue media outlets that report on Mr. Navalny’s allegations.

Ms. Rybka’s last update from jail on Wednesday said that “if we go back to Russia we will die in Russian’s [sic] prison or they will kill us.”

One hour earlier, Ms. Vashukevich wrote: “Please USA help us not to die from Russians!”

Mr. Navalny, whom the Kremlin has barred from running in the March 18 Russian presidential election, “used our videos for his investigation” against various Russians, she said.

“In my book ‘Who wants to seduce a billionaire’ there are many facts that hurt influential people of several countries,” she wrote on Feb. 23.

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