Measuring 21m by 13m, the billboard was to show a stylised bomb and fuse, decorated in stars and stripes, with the message: "Democracy is best taught by example, not by war."
Project Billboard, a group that says it is devoted to "diversity, tolerance and free expression," says it signed a three-month contract for the space beginning on 2 August.
But Clear Channel Spectacolor, which leased the space to the group, objected to the message, according to papers filed in the Manhattan federal court by Project Billboard.
The contract allows Clear Channel to reject the billboard if it is obscene, "misleading or deceptive" or "offensive to the moral standards of the community," court papers say.
A lawyer for Clear Channel told a federal judge on Tuesday that the media group "has concerns about the bomb image".
"Those of us who have been in New York for a while understand the sensitivities that many New Yorkers have to bombs," said the lawyer, Robert Pees.
The billboard space is on the side of the Marriott Marquis hotel. Clear Channel leases the space from the hotel.
Project Billboard initially offered to replace the bomb with a dove, keeping the text the same, but Deborah Rappaport, a board member for the group, said that offer no longer stands.
"Those of us who
have been in New York for a while understand the sensitivities that many New Yorkers
have to bombs"
lawyer for Clear Channel
"What we want is our billboard up," she told reporters.
In addition, Pees said Marriott must approve the billboard, and that the hotel had an "explicit" opposition to political advertising.
Clear Channel was willing to offer another space in Times Square, Pees said. Rappaport said Project Billboard would be willing to accept another space.
The judge made no immediate ruling, and scheduled another hearing for Thursday.
The four-day Republican National Convention begins on 30 August at Madison Square Garden, about 10 blocks south of Times Square.
Clear Channel, the nation's largest radio chain, has been accused of promoting right-wing politics and banning artists with whom it disagrees - including the Dixie Chicks, whose lead singer disparaged President George Bush.
The company is a major donor to Republican political candidates.
But it denies banning the Dixie Chicks from airplay and says pro-war rallies held by some stations during the Iraq war were the work of individual radio hosts and managers, rather than a corporate directive.