Victims of the 7 July London bombings will start to receive interim payments within the next 10 days, the Criminal Injuries Compensation Authority says.
Mr Blair said he would look into reports of compensation delays
The board said in a statement it had received 180 applications so far.
"We are working hard to make sure that victims of these terrible bombings receive the compensation... as quickly as possible," it said.
Prime Minister Tony Blair said at the weekend he would investigate reports survivors had yet to receive any help.
A dedicated team has been set up to deal with claims from bomb victims.
The Criminal Injuries Compensation Authority (CICA) said that "immediately on receipt of applications", police reports and medical reports had been requested.
"We received the first batch of police reports last Thursday and are now in a position to begin offering interim payments to victims within the next 10 days," the statement said.
A spokeswoman added there was a £500,000 cap on compensation, and that interim payments would be dealt with on a case by case basis.
"If someone has a specific injury then we would probably be able to give them an interim payment that equates to their pain and suffering," she told BBC News.
"Then we would look at the longer term, considering things like loss of earning... and then they'll receive their final payment."
Some survivors have expressed anguish at the length of time they have had to wait to receive compensation, which would allow them to avoid financial hardship.
It is more than 11 weeks since the blasts, and many of the injured said at the weekend they were concerned they had not yet received any money.
After hearing of the reports, Mr Blair told the BBC's Sunday AM programme: "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."
"The government should definitely help us," Martine Wright, 32, told the News of the World on Sunday.
Ms Wright, from London, had both legs amputated after the Aldgate Tube blast.
"I'm worrying about mortgages and things like that. I've enough to worry about at the moment with learning to walk again - this is an extra burden," she told the newspaper.
Some of the most badly injured in the Tube and bus blasts, like Ms Wright, are unable to work as normal and face an uncertain financial future.
Colin Ettinger, a lawyer representing 14 people affected by the bombings, said the compensation process usually took "a long time".
"The real problem is financial hardship, apart from the fact that they've got to put up with the injuries," he told BBC News.
"In the case of the fatalities, families have got to cope without their loved ones, which in some cases were the bread winners."
The £500,000 cap on payments would leave some families struggling in the long term, he added.