The government is to appeal against a ruling by the 7 July inquests coroner, who ordered MI5 evidence should be heard in open court.
Lady Justice Hallett ruled last week that she could not exclude the families from the hearings, despite pleas from government lawyers.
They argued that sensitive material concerning what MI5 knew about the bombers could only be heard in secret.
Families of victims said they were deeply angry and upset by the decision.
In a statement, the Home Office said that it had written to Lady Hallett saying that it would seek a judicial review of the decision not to allow closed evidence from the Security Service.
"The government has made clear that it welcomes the coroner's inquests," said a spokesman.
"We hope that they will allow the families of the victims to get to the bottom of the tragic events of 7 July 2005.
"This does not mean, though, that we will put lives at risk and undermine our national security by not protecting sensitive material. Therefore, having carefully considered the coroner's ruling on closed evidence, we have decided to appeal."
In a 46-page ruling delivered last Wednesday, Lady Hallett rejected the government's position that the only way to hear key parts of MI5's evidence was in secret.
Lawyers for the security service argued that coroners rules permitted all of the public to be excluded from hearings.
But Lady Hallett said that she would not order closed hearings because she had a legal duty to allow the families of the victims to attend.
In her judgement last week, she said: "I am still hopeful that with full co-operation on all sides, most if not all of the relevant material can and will be put before me in such a way that national security is not threatened."
But she also warned that should the government win an appeal to hold secret sessions, it could bring the entire process to a grinding halt.
"There remains the very real possibility that these inquests would have to be adjourned and the whole process restarted - I emphasise the word 'restarted', not 'resumed' - at a much later date under a different person."
Graham Foulkes, whose son David was killed, accused MI5 of being "cavalier", leaving the families distressed and angry.
"It's shocking that we hear this from the media and that MI5's barristers don't have the decency to tell our legal teams first," he said.
"To say we're upset is an understatement."
And Julie Nicholson, whose daughter Jennifer was killed in the attacks, accused MI5 of showing a "lack of respect" to the families.
"I wish that they would work with the inquest and help, like so many of these wonderful people we are hearing stories from," she said.
Clifford Tibber, one of the lawyers representing families, said the decision was "outrageous".
"The coroner has already said that there are no circumstances in which she will allow the personal safety of any member of the Security Service or the interests of national security to be put at risk," said Mr Tibber.
"The prime minister and the deputy prime minister are both on record as supporting a public inquiry. The Government have twice failed to introduce legislation to hold inquests in secret and now they are trying to introduce it through the back door. What have they got to hide?"