"With his health apparently deteriorating rapidly with each passing day, it is time to act. And fast," the open letter published on Monday declares.
"To do nothing would be to let Oleg Sentsov die," it claimed and called on the EU and UN to pressure Russian President Vladimir Putin into freeing him.
Sentsov, 42, is serving a 20-year sentence after being convicted of terrorism almost three years ago.
In a trial that "blatantly failed to respect the rights of the defence", according to the letter, he was found to have committed arson in his native Crimea when Russia annexed it from Ukraine.
Held in Siberia
He is being held in a prison in northern Siberia, leading the statement to compare his fate to that of author Alexander Solzhenitsyn, who spent seven years in a Soviet gulag.
Sentsov's lawyers say he has lost 14 kilos since starting his hunger strike on 14 May and on Friday said he was "ready to die".
Last week his cousin warned that his health was "catastrophically bad", prompting French President Emmanuel Macron to take up his case in a telephone call with Putin.
The Russian authorities deny that his condition is serious.
The prison service said he was "not seen to be underweight and a worsening in his state of health is not observed" in a statement on Saturday, adding that his health is "satisfactory" and "all necessary measures", including giving him nutritional supplements, are being taken.
Sentsov has refused to be taken to hospital.