The letter from a boy named Maxim in the hardscrabble industrial Urals city of Chelyabinsk came two weeks after Putin signed into law a bill banning all US adoptions.
The measure was given fast-track approval and almost no parliamentary debate in reprisal for new US legislation that targets alleged Russian rights abusers.
But the law also created controversy at home and is expected to see up to 20,000 people come out on the streets of central Moscow in protest this Sunday.
The teen's letter was published by Chelyabinsk media, which said that the boy had communicated with the Wallen family of the Atlantic Coast state of Virgina for seven years and that his case was already under court review when Putin signed the ban into law on December 28.
"I would be very grateful if you come out in favour of children," the website of local Chelyabinsk television quoted Maxim's letter as saying on Thursday.
"Put everything under strict control, but do not deprive children of their right to obtain a family," the boy reportedly wrote.
The media did not identify the disease from which the Maxim was suffering, saying only that it requires treatment not available in the country.
The Kremlin's local children's rights representative said the teen was close to his prospective family but the chances of Putin changing his mind on the law seemed remote.
"Maxim has strong relations with his American family and I do not think those bonds should be broken," the Chelyabinsk.ru website quoted envoy Margarita Pavlova as saying.
"It is hard to say how the situation will develop from here. Perhaps they will adopt some amendments to the law," she added in reference to Maxim's chances of leaving Russia.
"But the probability is very low."
She described the Wallens as caring and attentive -- two qualities missing from Maxim's children's home.
"There is a chance to treat Maxim in America and the Wallens are willing to pay," she said. "He could get a good education in that family."
Russian authorities have been lashed by critical media and the US government for the law, which critics say turned children into pawns of high-stakes diplomatic games.
But Putin has defended the measure and the national media released on Thursday interviews with the children's home director denied that the boy was either sick or wrote the letter.
"He has no genetic disease either," Children's Home No. 13 head Denis Matsko told Business FM radio. "He has certain health problems -- just like we all do."
A parliamentary cosponsor of the Russian adoptions legislation said she believed the letter was genuine but said adults likely made Maxim write it to make Russia look bad.
"This is all being done in order to make Russia look bad again," ruling United Russia party member Yekaterina Lakhova told the state RIA Novosti news agency. "To provoke a child like that -- I just cannot imagine how someone could do that."
Foreign adoptions are a sensitive issue in Russia because the practice of adopting has never truly taken hold among Russians themselves.
The Soviet Union raised all disadvantaged children together in vast collective homes, many of which continue to operate today across the country.
Most foreign adoptions are made by Americans -- nearly 1,000 were recorded last year -- while Russia is the third-most popular country for US nationals seeking to adopt.
Putin's law terminated the processing of nearly 50 cases that had been under review by the Russian courts.