The New York Post said the incident took place Tuesday night at Avery Fisher Hall.
"Ladies and gentlemen, I apologize for this. Usually when these things occur, we ignore them. But this is such an egregious disturbance that I am forced to stop," the Post said Gilbert told the audience, turning toward the front row where the offending phone was located. "Would you please just admit it? It's OK, just turn it off. Is it off now?"
The newspaper said some concertgoers yelled, "Throw him out!" referring to the phone's owner and cheered Gilbert as he resumed the performance.
"Alan's main concern was for the audience," Philharmonic spokesman Eric Latzky told the Post. "And to have this most beautiful, and this most delicate, symphony stopped by an iPhone at its most vulnerable moment -- [that] was what Alan was really concerned about, for the other 2,750 people in the hall."