The Prime Minister's promise came after survivors, and the relatives of the 52 people killed in the blasts, protested they had not received any cash from the Government.
Some said that they have to live on charity hand-outs because of delays in the criminal injuries compensation scheme.
Mr Blair told the BBC's Sunday AM programme that he would investigate their complaints.
"I think what is going to happen now is that over the next couple of weeks those payments are going to be made," said Mr Blair.
"It's the Criminal Injuries Compensation Board that primarily handles this and, obviously, they're an independent board."
He added: "Given those stories that are there today I'll look into this obviously myself - but I'm sure that they'll make the payments as soon as they possibly can."
It is understood the board began calculating levels of compensation last week, with interim payments beginning to be sent out by mid-October.
Three months is a typical wait for cash to be paid to the victims of crime, leaving some survivors dependent so far on the London Bombings Relief Charitable Fund.
Many victims of thebombings are still waiting for compensation, such as Garri Holness, who lost his leg in the King's Cross Tube bomb. Martine Wright, 32, from London, who lost both legs in the Aldgate bombing, told a Sunday newspaper: "I'm worrying about mortgages and things like that Victims shouldn't have to fight for compensation. I've enough to worry about at the moment with learning to walk - this is an extra burden. The Government should definitely help us"
n Mr Blair also defended proposals to detain terrorist suspects without charge for up to three months. He said: "If the police and security services are saying this really will make a difference to our ability to stop this terrorist threat, I don't think we can be in a situation of refusing that unless there is a very good reason.
"There is no question of this being three months without charge, without trial and with no judicial oversight. There would have to be continual judicial oversight."Reuse content