Chancellor Gordon Brown has left open the option of postponing the rises in fuel duty due in September.
Good news from Opec could curb rising fuel prices
Mr Brown said the focus should be on persuading oil exporters cartel Opec to get world prices under control, but he would review progress in August.
Opec has agreed to raise production by two million barrels a day. Mr Brown called that a welcome first step but argued more could be done.
Opposition parties want the 1.9p-a-litre planned duty rise to be scrapped.
Mr Blair said on Thursday the government had to see how the situation settled down after Opec's announcement on increasing oil production.
Asked on Thursday evening whether he was ready to respond to pressure to abandon the duty rises, Mr Brown told BBC News he had already postponed increases until September.
"Once I see the progress that is being made by Opec in raising production and getting the oil price under control I'll review the situation in August," he said.
"I want the focus of the next few weeks to be on where the source really lies, and the source of the problem is inadequate production and the instability in the Middle East."
The chancellor argued it would be "opportunistic" to move the focus away from the hikes in world oil problems.
He promised to continue to put the case for high production to oil ministers.
Haulage firms are warning the government to prepare for a series of protests if the cost of petrol and diesel does not come down.
Police say they expect about 300 lorries to converge on Cardiff for a demonstration over high petrol prices on Saturday.
Earlier Transport Secretary Alistair Darling said governments prepared for "all sorts of eventualities", but the UK had not reached a crisis point yet.
He was speaking after the Daily Express said leaked Department of Trade and Industry (DTI) documents showed secret government plans to deal with a potential crisis.
The paper says Britain could be put on a three-day week, drivers could face bans or face petrol rationing and sporting events like Wimbledon could be cancelled.
Mr Darling told BBC Radio 4's Today programme: "Some people - like [Tory leader] Michael Howard - wish to almost provoke these difficulties."
Mr Howard told BBC's Five Live: "I don't think there should be the kind of protest which would disrupt people's lives and stop people going about their law-abiding activities."
His message to Mr Brown was simple: "Do not put fuel duty up in September."
'Worst case plans'
For the Lib Dems, Mr Kennedy accused Michael Howard of "reprehensible gesture politics" for saying he might back protests.
A DTI spokesman said it would not comment on the leaked document.
But he said there were "contingency plans in place in case of worst-case scenarios to make sure there is no disruption of supply".
The average cost of a litre of unleaded petrol on Wednesday was 82.82p - up nearly 2p on the previous day - and some petrol stations were charging more than
90p a litre.
If prices continue to rise, the average UK price of petrol could approach the 85.32p recorded in June 2000, which sparked widespread fuel protests.