ROTHLEY, England (CNN) -- Madeleine McCann's father says the return of his family to Britain without his missing daughter is heartbreaking but it does not mean they are abandoning the search for her.
Kate and Gerry McCann arrive at East Midlands airport in England, Sunday with their twins.
Gerry McCann also insisted Sunday he and his wife Kate played no part in the disappearance four months ago of Madeleine despite being named by Portuguese police as suspects in the case.
The McCanns flew from Faro in southern Portugal with their two-year-old twins Sean and Amelie. At East Midlands airport in central England, Gerry McCann said the events of the last few days had been deeply disturbing.
"While it is heartbreaking to return to the UK without Madeleine, it does not mean we are giving up the search for her," he said. The McCanns, their friends and relatives say they are holding out hope that Madeleine is alive and will be found. Watch as Gerry McCann describes return home »
"We have played no part in the disappearance of our lovely daughter Madeleine," he added.
The family then traveled to their home in the Leicestershire village of Rothley, 170 kilometers (110 miles) north of London, where dozens of TV camera crews and journalists were waiting.
Madeleine's aunt, Philomena McCann, said it was "unbelievable" that the couple had been named as suspects, and urged the police to focus their investigation on finding the little girl.
"No-one believes the Portuguese police," she told GMTV. "To think they are so callous and psychopathic that they could have done that... two more loving parents you could not hope to meet."
In a separate interview with the BBC she said the family wanted the "investigation changed round to look for Madeleine alive, as we reckon she is."
She added that the parents were prepared to return to Portugal to under go further questioning.
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 they had left the girl and her siblings asleep in the unlocked apartment as they dined just meters away, checking on them frequently. However, later in the evening they discovered she was missing.
The case became a sensation in the British press and then internationally, with celebrities, including soccer icon David Beckham, offering their help. The parents traveled abroad to drum up support and even met Pope Benedict XVI.
But on Friday police in Portugal named the couple suspects after finding Madeleine's blood in a car the family rented 25 days after reporting her disappearance, a family spokeswoman said.
Officers in Portimao put the couple through intense rounds of questioning over the past few days, and declared them "arguidos," which, under Portuguese law, allows investigators to pose certain types of questions.
Arguidos also get certain legal protections that are not extended to mere witnesses. The term "arguido" is generally translated as "suspect." Portuguese authorities have not commented on the investigation.
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.
"I would like to emphasize that their return is with the full agreement of the Portuguese authorities and the police," McGuinness added.
The McCanns have consistently denied any wrongdoing.
In an interview published in the Sunday Mirror, Kate McCann is quoted as saying of the Portuguese police, "They want me to lie -- I'm being framed."
Philomena McCann told the British news network ITN that police "tried to get Kate to confess to having accidentally killed Madeleine by offering her a deal through her lawyer" in which she would say she killed Madeleine by accident "and then disposed of the body."
The Sunday Mirror quoted Kate McCann discussing the offer.
"They are basically saying, 'If you confess Madeleine had an accident, and that I panicked and hid the body in a bag for a month then got rid of it in a hire car, I'd get two or three years' suspended sentence,'" she is quoted as saying, adding, "Police don't want a murder in Portugal."
The paper also quoted her as saying Portuguese police don't want "the publicity about them not having pedophile laws here, so they're blaming us." The U.S. State Department's latest annual report on human rights practices in different countries calls the Portuguese government "strongly committed to children's rights and welfare," and cites the "high-profile trial of a pedophilia operation" in Lisbon.
Numerous friends and relatives of the McCanns have called any allegations of them having harmed the girl ridiculous.
On Saturday, Kate McCann's mother Susan Healy told ITN, "It's ludicrous. It's bizarre ... Kate never raises her voice to her children. She's the most loving and gentle mother."
"She's kind, gentle, funny, she has a good sense of humor -- a person with a good sense of integrity, as is Gerry," Susan 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
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