However John McCain, the Republican presidential hopeful, is still expected to address the convention on Thursday at the end, officials said.
McCain ordered most activities on Monday, the first day of the convention, to
Instead Laura Bush, wife of the current US president, will unveil video appearances from several governors of Gulf coast states, after the convention opens later Monday.
McCain will then ask for delegates for help and donations for the relief efforts once the storm has passed, said Rick Davis, McCain's campaign manager.
"We will try not to overly politicise it, but we felt it was important to encourage support into these areas," Davis said.
A short session took place to begin the legal procedures needed to officially nominate the candidates for the November 4 presidential election - McCain and Sarah Palin, governor of Alaska and the vice-presidential candidate.
The party has been swift to alter its convention plans in a bid to avoid being seen as holding a political celebration while Hurricane Gustav hits the south of the country.
Al Jazeera's Rob Reynolds in St Paul says both McCain and his Democratic rival, Barack Obama, are trying to appear above the partisan fray by telling Americans to work together to assist those affected by the hurricane.
Bush and Cheney's absence will also assist McCain as their appearance could reinforce in voters' minds the connection between the two men at a time when McCain is making his own bid for the White House, our correspondent adds.
McCain said on Sunday while visiting a hurricane relief centre in Mississippi that the party will "take off our Republican hats and put on our American hats and ... say 'America we are with you.'"
He also visited a disaster centre in Waterville, Ohio, during campaigning on Monday.
Earlier on Sunday police also arrested nine people taking part in large anti-war protest for tresspassing after they crossed a security fence into a restricted area near the Xcel Energy Centre where the convention is taking place, security officials said.
A much larger anti-war protest is planned for Monday, organisers say.