Mohammad Sidique Khan's family say they believe the Circle Line bomber could have been "brainwashed" by terrorists.
Mohammad Sidique Khan was a teaching assistant in Leeds
In a statement, they described the 30-year-old teacher as "a kind and caring member of our family" and appealed to the public for information.
"We are devastated our son may have been brainwashed into carrying out such an atrocity."
On Friday, the family of 18-year-old bomber Hasib Mir Hussain also said they were "devastated" by what had happened.
The Khan family's statement said they "would like to sincerely express their deepest and heartfelt sympathies to all the innocent victims and their families and friends affected by this horrific and evil act.
"We urge people with the tiniest piece of information to come forward in order to expose these terror networks which target and groom our sons to carry out such evils."
Mohammad Sidique Khan: Aged 30, from Beeston, Leeds, recently moved to Dewsbury, married with baby. ID found at Edgware Road blast site.
Hasib Mir Hussain: Aged 18, lived Holbeck, Leeds. Reported missing on day of bombings. Said to have turned very religious two years ago. ID found in No 30 bus.
Shehzad Tanweer (above): Aged 22, born Bradford, lived Beeston, Leeds. Studied religion in Pakistan. Forensic evidence linking him to Aldgate blast.
Germaine Lindsay: Jamaican-born man who lived in Buckinghamshire.
A teaching assistant at Hillside Primary School in Leeds since 2002, Khan lived in the Beeston area until recently, when he moved to Lees Holm in Dewsbury.
He is believed to have been married with a very young daughter, with newspapers naming his wife as teacher Hasina Khan.
The Hussain family's statement described the bus bomber as "a loving and normal young man who gave us no concern".
"We had no knowledge of his activities and, had we done, we would have done everything in our power to stop him."
Hussain was reported missing by his family in the aftermath of the bombings.
"We, the family of Hasib Mir Hussain, are devastated over the events of the past few days," they said in Friday's statement.
"We are having difficulty taking this in.
"Our thoughts are with all the bereaved families and we have to live ourselves with the loss of our son in these difficult circumstances.
"We had no knowledge of his activities and, had we done, we would have done everything in our power to stop him.
"We urge anyone with information about these events, or leading up to them, to co-operate fully with the authorities.
"This is a difficult time and we ask you to let us grieve for our son in private."