Mr Straw said he was considering wide-ranging reforms to the electoral procedure, including the introduction of electronic balloting and a switch to weekend polling days to make voting more family-friendly.
The final recommendations of the electoral procedures working party, headed by the Home Office minister George Howarth, will be published today. The working party will also suggest that local and European elections should take place on the same polling day to combat voter fatigue.
Mr Straw stressed during Question Time in the Commons that current voting arrangements could "inconvenience families".
He said: "I would also add, as I know it has been a problem in certain polling areas of the West Midlands, that I believe that there is no excuse for returning officers to seek to prevent parents with young children from entering the polling station and having to leave their young children outside the polling stations.
"We need to be doing - particularly against the background of reducing turn-outs - everything we can to encourage people to vote and to make it easier and not harder for people to vote."
Mr Straw said there was "nothing magical" about the use of Thursdays as polling day. "Saturday was used for elections in certain urban districts up until 1974," he said.
But the Home Secretary stressed he would want to ensure any new arrangements would not be open to electoral fraud.
"The transaction involved in voting with a pencil cross on a piece of paper now appears to many people to be very old fashioned, to be inconvenient. Polling stations are not necessarily sited in convenient places.
"I certainly am very keen on seeing an extension of postal voting for almost anybody who wishes it."Reuse content