Birmingham MP Khalid Mahmood, who grew up in the Sparkhill area, said a small number of militants in Britain had been "brainwashed".
The MP said he was shocked at reports of an alleged plan to film a victim being beheaded. But he added: "Looking at some of the films available on the internet already, and at the way things have been moving, I think it is possible."
He added: "These people are very much deranged and brainwashed by some of the people that are coaching them. We have to be very vigilant about this and this is why we have to offer our support to the police."
He said it was likely some of those arrested would be released without charge. This has led to complaints in earlier terror cases, where some Muslims have accused police of arresting too many people.
But Mr Mahmood (Perry Barr) said: "We have got to balance these issues against the safety and security of the public. The police are doing what they need to do."
Speaking in Stratford Road, near to where he grew up, Mr Mahmood urged local people to help the police inquiry.
The Labour MP, who attended primary and secondary schools in the Sparkhill area, said: "A lot of people are concerned that there have been people from within the Asian community that have been arrested.
"We have to make sure that the community comes forward very, very quickly to help the police."
The MP, who was briefed by a senior police officer, said he was told that the arrests followed six months of surveillance.
His fellow city MP Roger Godsiff (Lab Sparkbrook & Small Heath) said: "I'm totally supportive of the police in the operations they have carried out.
"They have done this based on intelligence information they have received."
He added: "Police have an extremely difficult job to do, and all law-abiding people who want to live in a safe society should support the police in trying to apprehend people who are trying to destroy society.
"This is a view shared by the overwhelming majority of my constituents, including my Muslim constituents."
Coun Salma Yaqoob (Respect Sparkbrook) was doing the rounds of her constituency yesterday listening to the concerns of shopkeepers close to where arrests took place. She said the mood was one of shock and distress.
"I've had calls from local shopkeepers who have stores close to where the arrests took place.
"The reaction is a mixture but mainly shock and fear of a backlash. There is a high population of ethnic minorities in my constituency and a lot of attention is on us whether we like it or not, and the whole area can become tarnished – it was described in one report as 'a hotbed for radicalisation'. This is how the far right can gain ground."