Washington and Law were each cited for best actor performances in "Fences" and "Hamlet," respectively. Zeta-Jones was nominated for best performance by a leading actress in a musical, "A Little Night Music," and Grammer was nominated for lead actor in a musical, "La Cage aux Folles."
"What a thrill to be nominated! The experience of doing this incredible show and working every night with such a talented group of people has truly been one of the most rewarding experiences of my career," Zeta-Jones said Tuesday. "And now to be nominated for a Tony. In my dreams, I couldn't imagine a better way to make my Broadway debut."
"Fela!" -- nominated for best musical -- and "La Cage aux Folles" -- nominated for the best musical revival -- each received 11 nominations, followed by "Fences" with 10 nods.
Nominated for best play were "In the Next Room (or the vibrator play)" by Sarah Ruhl; "Next Fall," by Geoffrey Nauffts; "Red," by John Logan; and "Time Stands Still," by Donald Margulies.
Best musical nominations went to Green Day's "American Idiot"; "Memphis"; "Million Dollar Quartet"; and "Fela!"
"I am very proud and humbled by this extraordinary recognition of our work today," said Michael Grandage, artsitic director of Britain's Donmar Warehouse, who was nominated for directing "Red." John Logan's engrossing, often enthralling new play about art, an artist and the act of creation, received seven Tony nominations.
Besides Washington and Law, the actor-play nominees include Alfred Molina, "Red"; Liev Schreiber, "A View From the Bridge"; and Christopher Walken, "A Behanding in Spokane."
In the actress-play category, the nominees were Viola Davis, "Fences"; Valerie Harper, "Looped"; Linda Lavin, "Collected Stories"; Laura Linney, "Time Stands Still"; and Jan Maxwell, "The Royal Family."
Harper, whose play has closed, said the nomination was "bittersweet" because "Looped" had closed. "That was sad and disappointing but boy does this sweeten the pot," she said. "And we have a 10-week commitment in Toronto. So there is an afterlife for the play, and that's exciting."
The performers competing with Zeta-Jones for the actress-musical prize were Kate Baldwin, "Finian's Rainbow"; Montego Glover, "Memphis"; Sherie Rene Scott, "Everyday Rapture"; and Christiane Noll, "Ragtime."
Scott, also nominated with Dick Scanlan for best book of a musical for "Everyday Rapture," got the news Tuesday from her husband and she said they had a "celebratory vegetable juice" and soy muffin. What do the nominations mean to her?
"That I have to be forced to wear dresses, that's what this means," said Scott. "I'm really happy for this one, actually, because we created from nothing."
Besides Grammer, the actor-musical nominees were Sean Hayes, "Promises, Promises"; Douglas Hodge, "La Cage aux Folles"; Chad Kimball, "Memphis"; and Sahr Ngujah, "Fela!"
Nominees for featured actress in a play: Maria Dizzia, "In the Next Room (or the vibrator play"; Rosemary Harris, "The Royal Family"; Jessica Hecht, "A View From the Bridge"; Scarlett Johansson, "A View From the Bridge"; Jan Maxwell, "Lend Me a Tenor."
Featured actor in a play nominees included David Alan Grier, "Race"; Stephen McKinley Henderson, "Fences"; Jon Michael Hill, "Superior Donuts"; Stephen Kunken, "Enron"; Eddie Redmayne, "Red."
Redmayne said Tuesday that working in New York has been a great experience for a "newbie" British actor.
"From the beginning, I felt a sort of fear of being an impostor, of being a Brit bringing a New York play to New York," he said. "The way it's been embraced by people has been completely overwhelming."
Nominees for featured actor in a musical were: Kevin Chamberlin, "The Addams Family"; Robin De Jesus, "La Cage aux Folles";
Christopher Fitzgerald, "Finian's Rainbow"; Levi Kreis, "Million Dollar Quartet"; Bobby Steggert, "Ragtime."
Nominees for featured actress in a musical were: Barbara Cook, "Sondheim on Sondheim"; Katie Finneran, "Promises, Promises";
Angela Lansbury, "A Little Night Music"; Karine Plantadit, "Come Fly Away"; Lillias White, "Fela!"
"I am honored but also I am humbled, because it showed that we are ready for evolution," said Plantadit. "The show is being recognized by our nominations for us pushing forward dance into a new arena."
Twyla Tharp, who choreographed and conceived the dance musical "Come Fly Away," set to Frank Sinatra songs, competes for best choreography with Rob Ashford, "Promises, Promises"; Bill T. Jones, "Fela!"; and Lynne Page, "La Cage aux Folles."
Special Tony Awards for lifetime achievement were given to playwright Alan Ayckbourn ("The Norman Conquests," a trilogy of three plays that won the best play revival Tony last year), and actress Marian Seldes ("A Delicate Balance," "Three Tall Women," "Tiny Alice").
The Eugene O'Neill Theater Center in Waterford, Conn., will receive the regional theater award.
Winners will be announced June 13 during a ceremony televised by CBS from Radio City Music Hall.