Piven appeared Thursday at the session requested by the producers of "Speed-the-Plow," which the performer abruptly quit in December after his doctor said he was suffering from mercury poisoning.
But after hearing from both parties, a panel composed of Actors' Equity and Broadway League representatives were unable to reach the necessary unanimous decision. A joint statement issued by the union and the Broadway producers' trade association said "the producers have the right, as a next step, to proceed to arbitration."
The producers could not immediately be reached for comment.
Piven's spokeswoman, Samantha Mast, issued a statement saying: "Mr. Piven is hopeful that the producers will ultimately recognize that he did the right thing by listening to the instructions from his doctors ... who told him to stop the play immediately and undergo enforced rest, rather than continuing to perform and risk dire health consequences."
The 43-year-old Piven, the Emmy- and Golden Globe-winning star of HBO's "Entourage," departed the production of David Mamet's satiric comedy after his physician said he had high levels of mercury in his body.
In an interview with the New York Times after the hearing, Piven said his illness stemmed from eating fish twice a week for 20 years, not from consuming too much sushi, as some reports suggested.
"The biggest misconception was that this all came out of the blue in December and that I came down with this sushi-gate stuff," Piven told the Times.
According to the Times, Piven cried as he described the stress he felt about his health while struggling to continue with the show. "I've never missed a day's work or a rehearsal in my life," Piven told the paper.
Piven said he tried to work through the illness and insisted that partying had nothing to do with his early exit from the show.
"At times I was incapable of getting enough oxygen to get my lines out on stage, and sometimes I'd forget where I was in the play," Piven said. "This misconception that I was out partying was wrong."
When asked if he thought he'd get a chance to work on Broadway again, Piven was optimistic.
"This is the holy grail for any actor," he said. "I kind of can't wait to do it again. And I hope to."
"Speed-the-Plow" opened last October to generally enthusiastic notices and by the time the revival ended its limited engagement Feb. 22 at the Ethel Barrymore Theatre, it had recouped its $2.26 million production costs.
Three different actors - understudy Jordan Lage, Norbert Leo Butz and William H. Macy - followed Piven in the role of movie mogul Bobby Gould. Mamet's three-character play about Hollywood glamour, sex and power, also starred Elisabeth Moss of AMC's "Mad Men" and Raul Esparza.