The stars are set to perform at this weekend's (01-03Mar13) Java Jazz Festival, which is sponsored by tobacco firm Djarum.
The sponsorship deal has caused outrage, and activists want the singers to cancel their appearances at the show in Jakarta amid claims Djarum's involvement is glamorising smoking.
It comes as officials in Indonesia are preparing to introduce new legislation to limit the advertising of tobacco products and ban related companies from sponsoring music and sporting events.
Amanda Sandford, research manager for Action on Smoking and Health, says, "For decades the tobacco industry has used sponsorship to promote its brands to impressionable young people. Most countries have now banned this and in response, the industry has focused on exploiting the lack of regulation in countries like Indonesia.
"The fact that musicians and entertainers are willing to take (the tobacco companies') money adds to the problem. We call on all entertainers to make a public commitment not to accept tobacco money and to withdraw from any existing contracts."
However, David is refusing to axe his slot, with his spokesperson telling Britain's Independent newspaper, "We believe that allowing the advertisement of tobacco is an issue for the government of Indonesia to deal with via legislation.
"Craig is very much looking forward to entertaining his fans at Java... and believes that they are able to make their own decisions when it comes to this issue."