The award-winning TV star is up for best performance by an actor in a featured role in a play for his portrayal of pompous steward Malvolio in the revival of the Shakespeare’s Globe production, which transferred to New York last October.
Stephen faces his co-stars Mark Rylance and Paul Chahidi, who are also up for the same award.
Irish actor Chris O’Dowd has been nominated for his theatre debut in the Broadway adaptation of John Steinbeck’s Of Mice And Men, in which he stars alongside James Franco. Also vying for the gong are Rylance for his portrayal of Richard III in the play of the same name, Breaking Bad star Bryan Cranston and Tony Shalhoub.
British actress Sophie Okonedo has been recognised for her performance in A Raisin In The Sun.
There were acting snubs for some big names including Daniel Radcliffe, who has reprised his role in Martin McDonagh’s play The Cripple Of Inishmaan, Sir Ian McKellen and Sir Patrick Stewart, Denzel Washington, James Franco, Zachary Quinto and Michelle Williams.
The musical, A Gentleman’s Guide To Love And Murder, leads the nominations with 10 nods, followed by cult off-Broadway hit Hedwig And The Angry Inch, which stars former Tony host Neil Patrick Harris, with eight nominations.
After Midnight, a musical celebrating Duke Ellington’s years at the Cotton Club nightclub, received seven nods, tied with Beautiful: The Carole King Musical and Twelfth Night.
Michael Grandage, the director of The Cripple Of Inishmaan, has received a nomination for best direction of a play alongside fellow Brits Tim Carroll (Twelfth Night) and John Tiffany (The Glass Menagerie).
The nominations were announced by Lucy Liu and Jonathan Groff in New York, with Hugh Jackman making a surprise appearance.
Hugh will host the 68th annual Tony Awards, which will take place at New York’s Radio City Music Hall on June 8.