CAIRO, March 18 (Reuters) - Egypt has invited tobacco companies to bid for a licence to manufacture cigarettes in the country, according to the bid document, a move that could end a decades-old monopoly by the state-controlled Eastern Company .

The winning bidder must begin production within three years at a rate of at least 15 billion cigarettes a year, said the document, issued by the state Industrial Development Authority.

However four companies who were invited to bid said in a letter to the prime minister that the licence's conditions were too narrow, and called on him to halt the bid round until they could be made fairer.

They complained that as only one licence was on offer, the winning company would have an unfair advantage over its competitors.

The four companies that signed the letter were Nakhla Tobacco Co, Imperial Tobacco, British American Tobacco, and Al-Mansour International Co. For Distribution, all of which operate in Egypt.

The deadline for bids is April 4 and the auction will be held on June 6, the bid document said.

The cigarette industry contributes more than 60 billion Egyptian pounds ($3.8 billion) to government coffers yearly, the letter said.

($1 = 15.6300 Egyptian pounds) (Reporting by Ehab Farouk and Patrick Werr; Editing by Aidan Lewis and Jan Harvey)