Sheen and Janney, who played President Josiah Bartlet and press secretary C.J. Cregg on the NBC series, supported Hill at his play Monday on Presidents' Day.
Hill shared a pair of photos on Instagram with Sheen and Janney backstage. The actor portrayed Charlie Young, Bartlet's personal aide, on The West Wing.
"The President & the Press Secretary came to see Mr. Cole on stage... #WhatsNext? #MartinSheen #AllisonJanney #LightsOutGP #LinkInBio #NatKingCole #WestWing #lathr #NatsGuests #GeffenPlayHouse #PresidentsDay #Family," he wrote.
Janney also posted a picture with Hill, the actor's wife, actress Jazmyn Simon, and Kevin Gessay. She encouraged fans to see Hill in the play Lights Out: Nat "King" Cole.
"Unforgettable performance by @dulehill in #lightsoutgp #natkingcole Go see this play! @jazmynsimon @kgessay," the actress wrote.
The West Wing had a seven-season run from 1999 to 2006. Series creator Aaron Sorkin said in an interview with The Hollywood Reporter in November 2017 that he's considered rebooting the show. He suggested casting This is Us star Sterling K. Brown, with Sheen to reprise Bartlet in a guest role.
"Sterling K. Brown as the president, and there's some kind of jam, an emergency, a very delicate situation involving the threat of war or something, and Bartlet, long since retired, is consulted in the way that Bill Clinton used to consult with [Richard] Nixon," the producer said.
Sheen now plays Robert Hanson in the Netflix series Grace & Frankie, while Janney stars on the CBS series Mom. Hill portrays Alex Williams in the USA Network legal drama Suits.