Chief investigating police officer Olegario Sousa said at a news conference that police are looking for a white man, between the ages of 35 and 40, who was wearing a dark jacket and light beige trousers and who was possibly carrying a little girl on May 3 in Praia da Luz, the date and place where Madeleine disappeared.
"The man was carrying a child or an object that could have been taken as a child" Sousa told journalists. He also said the man was 5 feet, 10 inches tall and of medium build.
Madeleine disappeared May 3 after her parents left her and her brother and sister, 2-year-old twins, alone in their room while they went to a restaurant inside their hotel complex in Praia da Luz, a tiny resort town in Portugal's Algarve region.
Sousa urged anyone who might have seen the man to come forward and said police interviewed witnesses Thursday and Wednesday.
"The investigation is ongoing," Sousa said. "This description was given to us by one of the witnesses in the case."
Police had questioned Robert Murat, a 33-year-old British man, in the case but later released him, saying they did not have enough evidence to bring charges. Murat lives near the McCanns' hotel in Praia da Luz.
He said dozens of reports of Madeleine's possible whereabouts were still being checked.
Sousa also said that Interpol has supplied information to the investigation and much information was coming in from sources abroad.
Earlier on Friday, the parents of Madeleine said the guilt they feel over leaving her alone in a hotel room will haunt them forever. Gerry and Kate McCann, in an interview with Britain's Sky TV, also said they had no plans to return to Britain without her.
"I can't think about going home without Madeleine," said Kate McCann while holding a pink stuffed toy cat that had belonged to her daughter.
"Looking at it from where we are now," she said, "I don't feel we were irresponsible, I feel we are very responsible parents, you can't help but have emotions like that."
"For us it really wasn't all that different from having dinner in your garden in the proximity of the location," she said.
The family is concentrating on its Internet and media campaigns to publicize her disappearance across Europe. They are also hopeful about the outcome of an investigation jointly led by Portuguese and British authorities.
"So many people are doing so much to help us find Madeleine," Gerry McCann said. "We want Madeleine back and people can influence that," he said. "One evil act has resulted in so much good."
But the McCanns recognized that their lives have been seriously affected.
"Physically and mentally, we're shattered," said Kate McCann.
On Wednesday the McCanns prayed at the holy site in Fatima for her safe return.
Meanwhile, a senior official said earlier in the week that forensic tests on evidence in the case are still far from being completed.
The head of the National Forensic Medicine Institute, Duarte Nuno Vieira, denied reports that tests on hair, fiber and sweat samples taken from the hotel room where Madeleine disappeared had yielded no clues.