"I ask you, Vladimir Vladimirovich, to show mercy and grant pardon to Oleg Sentsov, do not destroy his life and that of his loved ones. We are waiting for him at home," she said in the letter dated June 22.
"We'll wait until we receive it," he told reporters. "It will certainly be considered," Peskov said, adding that he did not know if the formal appeal would lead to a pardon.
Sentsov is serving a 20-year sentence after being convicted on terrorism charges over an alleged arson plot in Crimea. His supporters say the case was trumped up.
Sentsov's mother said in her letter that her son had not killed anyone and wanted to dedicate his life to filmmaking.
"He has already served four years," she wrote.
"His children are waiting for him. His younger son is autistic. They are feeling bad without him. They will never be happy without their father."
Western governments and celebrities including Pedro Almodovar, Johnny Depp and Stephen King have repeatedly urged the Kremlin to release Sentsov.
"Your fight makes sense, well beyond the Arctic Circle or even Moscow where so many naive tourists, having come for football and beer, do not even know about your existence while it's also for them that you are fighting," wrote the author of "The Kindly Ones."
Moscow has shown little enthusiasm for letting the anti-Kremlin filmmaker go. There had been hopes he might be released as a gesture of goodwill by Sunday's World Cup final hosted by Russia.
However, lawyers say that a Russian president can pardon an inmate even if he or she does not formally ask for clemency.
Ukrainian President Petro Poroshenko said on Facebook his government would keep up pressure on the Russian authorities in a bid to free Sentsov and dozens of other Ukrainians it views as political prisoners.
Sentsov launched his hunger strike on May 14 to demand Russia release Ukrainian political prisoners.
Sentsov has lost around 15 kilogrammes, while he is being sustained with water and a glucose drip, his relatives say.
On average, humans can survive without food for about two months. Russian activists who staged pickets in Sentsov's support have been harassed by the authorities.
Today, an activist was sentenced to five days in jail for demonstrating in Sentsov's support in the second city of Saint Petersburg, officials said.
Sentsov is best known for his film "Gamer", which screened to critical acclaim at the Rotterdam Film Festival in 2012.
Supporters say Russia wanted to make an example of him with a particularly harsh sentence for masterminding arson attacks, which he denies.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)