The cover of the newspaper's Thursday edition featured a photograph of the two at the marathon, where two bomb blasts killed three people and injured more than 170. Media reports said investigators have video images of two suspects carrying black bags at each explosion site.
The picture in the Post was captioned "Bag Men -- Feds seek these two pictured at Boston Marathon." The accompanying story said federal investigators had been circulating the photo "in an attempt to identify the individuals highlighted therein."
One of the men shown in the photograph, Salah Barhoum, said on Facebook he was going to the police to clear his name.
"People think I did it. It's the worst feeling. I didn't do nothing," he told the syndicated TV show "Inside Edition."
"We stand by our story," Politico quoted Post Editor Col Allan as saying in a statement.
"The image was emailed to law enforcement agencies yesterday afternoon seeking information about these men, as our story reported," Allan said. "We did not identify them as suspects."
The Post has published incorrect reports on the bombing, including one that 12 people had been killed and one that authorities had identified "a Saudi national" as a suspect in the attack.