A family of 12 including two grandparents with health problems and a baby are feared to have travelled to Syria.
Police have launched an investigation after the group from Luton failed to return home from a holiday in Bangladesh.
Relatives say their disappearance does not make any sense, adding that they "can only think they have been tricked".
Muhammed Abdul Mannan, 75, and his wife Minera Khatun, 53, are missing, along with their 21-year-old daughter Rajia Khanom, 21 and sons Mohammed Zayd Hussain, 25, Mohammed Toufique Hussain, 19, Mohammed Abil Kashem Saker, 31, and Mohammed Saleh Hussain, 26.
Three unnamed children aged between one and 11 - a son of the older couple and two grandchildren - are with the group, as are Mohammed Abil Kashem Saker's wife Sheida Khanam, 27, and Mohammed Saleh Hussain's wife Roshanara Begum, 24,
Mr Mannan was described as "frail" and reportedly suffers from diabetes, while his wife is understood to have cancer.
In a statement issued through police, relatives of the group said they are "devastated" and "very concerned for their safety".
They said: "This is completely out of character and we are very worried of the danger they may now be in.
"Muhammed Abdul Mannan is elderly and both he and Minera Khatun have health issues.
"This just does not make any sense. We can only think they have been tricked into going there, it is no place for elderly or young people.
"We would urge any of them to please make contact with us or the police to let us know they are okay."
The party initially travelled to Bangladesh from Heathrow via Istanbul on April 10, before flying back to the Turkish city on May 11.
They were due to come back to London three days later but failed to return and were reported missing by a relative on May 17.
A police spokeswoman said: "There is a suggestion that the family may have gone to Syria, however police have so far been unable to corroborate that information.
"Police are continuing with their inquiries and are working with relatives who are still in the UK."
Community leader Ashuk Ahmed described the family as "nice, polite and caring" and said he had known them for around 30 years.
He said there were suggestions within the community that a woman in the group might have been "radicalised". Police have not commented on the claims.
Mr Ahmed told the Press Association he understood that one of the reasons the family had travelled to Bangladesh because of Mrs Khatun's cancer.
He said: "The family was under the impression they were travelling to Bangladesh. It was planned as a genuine family visit.
"They were told that no one knows what might happen so they might as well go and visit their family in case things get worse and on that basis they flew out the whole family.
"The community is in shock."
He added that he had heard suggestions that a member of the group had contacted relatives a few weeks ago.
"I was told by people in the community that they made a phone call to family members and told them not to worry and that they were safe."
Mr Ahmed, who was the Lib Dem parliamentary candidate for Luton South at the last election, said Mr Mannan's sons were successful plumbing and electrical contractors.
He said: "I have spoken to one of their business associates, they still have work to finish and have taken many new jobs on, so surely it would be the last thing on their minds to take on new business.
"This is not a family I would have ever have suspected of that, they would probably be the last on my list."
He explained that Mr Mannan had worked in a factory before retiring and had three children with his first wife before she died, while Mrs Khatun is a housewife.
Mr Mannan's children who are suspected to have travelled to Syria were all his current wife's, Mr Ahmed said.
Forid Chowdhury, a community worker who has lived in the same area as the family all his life and known Muhammed Abdul Mannan for over 30 years, said he was "shocked and devastated" by the news.
Mr Chowdhury said that he was not aware of any members of the family getting involved with extremist organisations or marches against British foreign policy in Luton.
Rumours about the family had been going round for "three or four" weeks, he said.
He described Mr Mannan, who worshipped at Bury Park Jame mosque in Luton, as a "very simple, very pious" man.
Mr Chowdhury, 34, said: "If it is true I appeal to his (Mr Mannan's) children to consider their elderly father and the mother, return and contact the local authorities.
"These are elderly people, respected people in the community and they need medical help and treatment.
"It is not normal for somebody of their age with their grandchildren to be missing for so long.
"The community as a whole are shocked and worried and concerned for their safety.
"I can't really speak for the mother but the old man is very simple and very humble and he was a very quiet person in the mosque, a spiritual and pious person.
"Everyone loves the old man in the mosque, he is highly regarded.
"As for the family themselves, we have never had any problems with them or heard anything about them being radicalised or involved with extremists or anything like that."
Last month fears emerged that three British sisters had travelled to Syria with their nine children aged between three and 15.