Russian Prime Minister Vladimir Putin, center, visits the home of Dasha Varfolomeyeva, left, in the village of Tugnui, in the southeastern Buryatiya region in July. Two years ago, Dasha asked Putin during a live televised Q&A for the present of a dress from a fairy tale. (Alexei Druzhinin/ASSOCIATED PRESS)

The elevators in the state Children’s Hospital in the city of Elista don’t work, so after his 6-year-old daughter was anesthetized, Andrei Godin gathered her in his arms and walked down four flights of stairs to deliver her to the operating room.

When the doctors finished their surgery, Godin recounted, he picked up Polina and carried her to her room, up four flights in a paint-peeling, graffiti-streaked stairwell. By the time he put his limp daughter back in her hospital bed that May morning, Godin knew drastic action was required. Someone had to do something about the shabby, dirty hospital, the only one for children in Kalmykia, a region 1,200 miles south of Moscow.

Soon after, he recalled in a telephone conversation, he signed an online petition begging U.S. President Obama to take the hospital under his care and fix it up. More than 300 parents in the small capital city of Elista did the same, and the letter was sent to the U.S. Embassy here in Moscow last week for forwarding to Washington.

“We are desperate,” Godin said. “The operating room is dirty, the wards have bare electrical wires coming out of the walls, and mothers who stay with their children have to sleep in their beds with them. No one will do anything. That’s why we appealed to Obama.”

The letter may be addressed to Obama, but the petitioners are using it to pressure their own leaders to listen to them, convinced that if they only knew what was going on, something would be done, a belief that has been cherished throughout Russian history. Once such hopes rested with the czars; today they are directed toward the ruling tandem, Prime Minister Vladimir Putin and President Dmitry Medvedev, who have modernized the process.

In addition to piles of letters, Medvedev gets tweets and Putin has an annual televised call-in show, where just three years ago a poverty-stricken 9-year-old Siberian girl appealed for a Cinderella-like dress. Putin invited the entire family to Moscow for tea and gave the girl and her sister party dresses. This July, he visited the village to check on the economic development he had ordered, and gave the now 12-year-old a laptop. That kind of response is rare, but well publicized.

“There’s a certain letter machinery,” said Boris Altshuler, a Moscow human rights activist since the 1970s who offered to get the letter from Kalmykia to Obama, by way of the U.S. Embassy. “It’s like putting a note in a bottle and throwing it into the ocean.”

The residents of Kalmykia, Europe’s only predominantly Buddhist enclave, were tired of waiting. Appeals had been sent along the governmental chain of command, but the parents didn’t know whether anyone had heard. Money had been allocated to repair the hospital in 2008, commemorating the 400th anniversary of Kalmykia’s entrance into Russia. The work was supposed to have been finished in 2009. Many assume the money was stolen or misappropriated — always the first assumption when government disappoints here.

“There is a firm belief that power is very corrupt,” said Boris Dubin, sociopolitical director of the polling group Levada Center, “that they do for themselves and don’t care about people. And there is a parallel three-quarters of the population that trusts Putin and Medvedev. People believe the leaders are good — the czar is good but the boyars [nobility] are bad.”

Sandji N. Buvaev, a Web-savvy Elista resident who runs a tourist agency, helped organize unhappy residents online, where they had been posting complaints late last year on a forum about the hospital.

In December, Buvaev said, the parents got the attention of Pavel Astakhov, Russia’s children’s ombudsman. He was touring the area, heard about the hospital and changed his schedule to make a visit.

“He was shocked with what he saw there,” Buvaev said, and met with the head of the regional administration, then sent a report to Medvedev. But at the end of June, with no results, the parents decided to send a letter to Obama and began collecting signatures.

“We appealed to him because he is believed to be a guarantor of human rights,” Buvaev said.

The parents, trying to shame their officials into action with the letter, understand they risk antagonizing them — Russia emphatically does not like the United States to tell it what to do. But they are desperate. “Irritation doesn’t matter,” Altshuler said. “Our goal is to make them irritated so they’ll do something. I am sure there will be positive impact, but only if there is a sufficient campaign.”

Though the head of the local administration was changed last year, Godin pointed out that Kalmykia has had a history of poverty and corruption. It was run until last fall by Kirsan Ilyumzhinov, a millionaire who once reported that he was abducted by aliens.

Ilyumzhinov, the head of FIDE, the world chess federation, was in Libya in June playing chess with his friend Moammar Gaddafi.

Godin said Ilyumzhinov was always more interested in chess than hospitals, building an expensive development called Chess City in Elista to attract world championship games, while citizens complained that their needs went unmet.

The one bright spot, Godin said, was that his daughter recovered well from her surgery. “It’s only because of the doctors,” he said. “The doctors and nurses are wonderful. They stay and take care of our children despite the terrible conditions. They know our children are sacred to us.”