MOSCOW—Fugitive former intelligence operative Edward Snowden told supporters at a secret dinner this week that he doesn't regret leaking details of classified U.S. surveillance programs, despite having to live his life on the run because he is satisfied his actions have had an impact, a person present at the dinner said.

Mr. Snowden told four former U.S. government agents-turned-whistleblowers, who traveled to Moscow to give him an award, that he was settling into his new life in Russia and was happy to have avoided the fate...