The support for the draft was announced by Democrat leader Abhisit Vejjajiva after a meeting of a party working committee to sound out the party's stand on the draft.
Abhisit said the Democrat saw that the new constitution would be similar to the 1997 charter but it would have many improvements to enhance public rights and political participation.
Speaking to a press conference after the meeting, Abhisit said the overall structure of the draft was similar to the 1997 constitution, especially provisions related to civil rights and liberty, independent organisations and parliamentary system.
But the new draft has been designed to tackle political problems occurred during the enforcement of the 1997 charter while there are provisions to better protect and enhance civil rights and liberty, he said.
Abhisit added that the draft would also add the public check-and-balance power through parliament while enhancing voters' participation in politics by making it easier for them to file impeachment motions against political office holders and to propose new laws.
He said the draft also tackled some drawbacks of the 1997 constitution by allowing non-university decree holders to contest elections and allowing Cabinet members to retain their House seats.
He said the draft would also improve the budget making by the government and enhance the significance of local administrations.
The Democrat leader said his party would prepare documents on the pros and cons of the draft to distribute to the people through party branches and members nationwide.
"It will not be a campaign for the public to accept the draft but we will simply inform the public about the pros and cons of the draft," Abhisit said.
He said the Democrat was not trying to please the Council for National Security by announcing support for the draft.
"If we want to please the CNS, we must reject the draft so that the CNS can select a previous constitution for use. If we reject the draft, it will be like handing out the power to the CNS. We have come up with this stand because we care about the national interest and want the democracy to be restored as soon as possible," he said.
Abhisit said if the draft was rejected in the public referendum, the next election would be delayed by at least another month.
Prime Minister Surayud Chulanont, meanwhile, denied that soldiers had been instructed to launch campaigns for voters to vote for the draft in the public referendum.
"It's not true," Surayud said when asked to comment on an allegation made by Chaturon Chaisang, leader of the Thai Rak Thai Group, that soldiers were instructed to campaign in support of the draft constitution.
"We are not trying to influence the outcome of the referendum."
He said he had met provincial people and most of them wanted to see the next election held as soon as possible.
"But the election must come after the public referendum," Surayud said.
The prime minister added that the public referendum bill would not force voters to vote for the draft either.
In a related development, Interior Minister Aree Wongsearaya said the Constitution Draft Assembly could seek help from Interior Ministry officials to launch awareness campaigns on the draft constitution.
He said the interior officials could also have their own stand on the draft as general people.