Anti-whaling countries including the US, the European Union and Australia want to tighten restrictions on whaling introduced by the moratorium.
But a three-quarter majority vote is required for major changes to the IWC convention regulating whaling, and the IWC is roughly split between whaling nations and their supporters and anti-whaling nations.
Japan, Norway and Iceland are also leading calls for an easing of the ban on the international trade in whale meat, and to prevent whales from being added to lists of endangered species.
Environmental groups and anti-whaling nations fear that other countries attending the summit, which runs until June 26, may join the calls for commercial whaling to resume.
The deep divisions between the pro- and anti-whaling camps have led to speculation that the IWC may break apart if whaling nations feel they are not being treated fairly and pull out of the body altogether.
Whales have been hunted commercially for centuries - both for their meat and their blubber, the oil from which was used for fuel.
But the hunting pushed many species to the brink of extinction, and a growing environmental movement lead to the IWC introducing a moratorium on commercial whaling in 1986.
Environmentalists say that while the ban has helped the world's whale population to recover to some degree, most species remain vulnerable.
|Up to 40,000 whales have been killed around the world since 1985 [Reuters]
Pro-whaling countries argue that whaling is part of their culture and say that sustainable whaling is possible.
Despite the moratorium, almost 40,000 whales have been killed worldwide since 1986 by countries which refuse to sign up to the IWC treaty, or which log its numbers under scientific or aboriginal headings.
At the last summit in the Chilean capital Santiago, the IWC set up a small working party charged with drawing up an interim deal on the most urgent disputes - including the definition of scientific, or "lethal research" purposes.
"These were some very tough negotiations," William Hogarth, the IWC's American president, told the Associated Press.
"So I am hoping that this meeting will outline the process so we can go forward."
Economics of whaling
During the conference the International Fund for Animal Welfare (IFAW), a global conservation group, is expected to present a report on the commercial advantages of using whales in tourism rather than hunting them.
In Madeira, itself once host to a thriving commercial whaling industry, local tour operators say whale-spotting now provides them with a steady income.
Last week, the World Wildlife Fund (WWF), another conservation group, said that Japan and Norway were giving large subsidies to their whaling industries, which have become unprofitable due to rising costs and the declining demand for whale meat.
In its report on the economics of whaling, the WWF said that Japan has spent $164m supporting its whaling industry since 1988, adding that the Japanese whaling industry needed $12m to break even in the 2009 season.
Margins are also tight in the Norwegian whaling industry, the WWF said, with low fixed prices and falling meat demand, a situation illustrated by the fact that the country has only taken around 70 per cent of its self-assigned 885-whale quota in recent years.