Protest organizer Andy Thayer says the request was identical to one already approved by the city for May 19. That parade permit was approved when the G8 summit also was going to be held in Chicago.
But the White House moved the G8 meeting to Camp David, leaving protesters with permits for a day when no meetings will be held.
"They're clearly playing a political game, and the people of Chicago should speak out against it," said Thayer.
Officials say the NATO gathering will be larger than the G8 would have been. There will be many more dignitaries arriving by motorcade on Sunday May 20 and a march down State Street toward McCormick Place could contribute to gridlock.