Senior officials from Egypt, Jordan, Saudi Arabia, Sudan and Yemen are meeting in the Egyptian capital, Cairo.
It comes amid a report that pirates who hijacked a Saudi oil tanker on Saturday are demanding a $25m (£17m) ransom.
However, the Sirius Star's owners, who are negotiating with the pirates, have cast doubt on that figure.
The Sirius Star, the biggest tanker ever hijacked, is carrying a cargo of 2m barrels - a quarter of Saudi Arabia's daily output - worth more than $100m.
It is now anchored off the Somali coast with around 25 crew members being held as hostages.
A pirate on board the vessel calling himself Mohamed Said was quoted by news agency AFP as saying that the Saudi owners, Vela International, had been set a 10-day deadline to hand over a $25m ransom.
BBC Security correspondent Frank Gardner says the owners are effectively denying that figure, while the industry is expecting the demand to be higher.
A spokesman for the Egyptian foreign ministry, Hossam Zaki, was quoted by Egypt's official Mena news agency as saying that "all options are open" in trying to solve the crisis. More...