The Cabinet Office Minister said people need to be aware there was a risk to fuel supplies but suggested "there was no need for rushing around in a mad dash".
His comments came as Downing Street has denied causing widespread panic about fuel supplies and David Cameron prepares to convene a cross-Government meeting to prepare for a tanker drivers strike.
Mr Cameron said at a press conference that there was no need to queue for petrol but should take sensible precautions to top up if there was a strike on the way. He said the potential strike was unnecessary as the drivers were not badly paid. He warned that a strike could cause enormous damage to Britain. The meeting of senior ministers from across Government departments will take place this afternoon to discuss plans to cope with a potential petrol crisis over Easter. Mr Cameron will chair the meeting in the room used for the emergencies committee, Cobra.
The Government's message to drivers to be prepared for a shortage at the pumps has been criticised by Labour, oil company Esso and the AA.
But a source at Number 10 has reportedly described ministers' warnings about the potential disruption as "gentle".