The shareholder, Mr Michael Iorio, filed the lawsuit in the Delaware Chancery Court and said company directors have a duty to get the best possible price for the shares and haven't considered possible higher bids.

"The directors failed to fulfil their obligations by not properly seeking the best alternative for the shareholders of Conoco and acting appropriately," Mr Iorio said in his lawsuit.

Last week, the two giants merged to form the third largest oil company in the US, which will be now known as ConocoPhillips. Phillips Petroleum is well known by Australians for its role in trying to develop Timor Sea vast gas reserves.