PORTIMAO, Portugal (CNN) -- Kate and Gerry McCann left Portugal for their home in Britain early Sunday after police officially named them suspects in the disappearance of their young daughter Madeleine.
The couple departed from Faro Airport with their two younger children on a plane bound for East Midlands Airport.
Their trip back home comes a day after police declared them "arguidos," which, under Portuguese law, allows investigators to pose certain types of questions and gives them certain legal protections that are not extended to mere witnesses. The term "arguido" is generally translated as "suspect."
The McCanns reported that Madeleine had gone missing days before her 4th birthday on May 3 from their holiday apartment in Praia Da Luz in southern Portugal. The parents told police that they had left the girl and her 2-year-old twin siblings asleep in the apartment as they dined just meters away. Watch CNN's Paula Hancocks report on the developments »
The girl's disappearance became a sensation in the British press and then internationally, with celebrities, including soccer icon David Beckham, offering their help to draw attention to the case and help raise money for the search. The parents traveled abroad to drum up support and even met with Pope Benedict XVI.
The couple had vowed to stay in Portugal to clear their name, but on Sunday family spokeswoman Justine McGuinness said the McCanns were "returning to Britain after careful thought" and to give their twins a more normal life.
"They played no part in the disappearance of their beloved daughter," she said in a statement to the media.
McGuinness said the McCanns, who live in Leicestershire in central England, were contemplating "their response to and future actions in relation to the events of the last few days which have been so deeply disturbing to them," a reference to the naming of them as suspects in the case.
"Their heartfelt plea is that the search for Madeleine should continue and that people should continue to remain vigilant," McGuinness said.
"I would like to emphasize that their return is with the full agreement of the Portuguese authorities and the police."
The McCanns have consistently denied any wrongdoing.
On Saturday, family and friends of the McCanns expressed disbelief that the couple would have harmed their missing daughter.
Kate McCann's mother called the suggestion "ludicrous."
"It's bizarre. ... Kate never raises her voice to her children. She's the most loving and gentle mother," Susan Healy told the British news network ITN in Liverpool.
"She's kind, gentle, funny, she has a good sense of humor -- a person with a good sense of integrity, as is Gerry," Healy said.
Kate McCann's father, who sat by his wife, said the couple has no idea what evidence might have led police to formally name Madeleine's parents as suspects in the disappearance.
"We all believe Madeleine is still alive, Brian Healy said.
A friend who has known Kate McCann for 30 years agreed that it was "unthinkable" that the McCanns would have harmed their child.
"I've not spoken to them in the last say two or three days, but I'm sure they're probably struggling," Nicky Gill told ITN in Liverpool.
"To even think that someone might harm the children. They're just family people. They love the children to death. ... I'm sure they have to be devastated to know someone would even think that."
Gill said she is convinced that the girl is still alive.
"I think she's out there somewhere. I like to think it's just a phone call away." E-mail to a friend