CAIRO, June 2 (Reuters) - Egyptian authorities have presented an amended invitation for tobacco companies to bid for a licence to manufacture cigarettes, a document seen by Reuters showed, after four firms complained the terms were too narrow.

The license could end a decades-old monopoly by the state-controlled Eastern Company which has a 70% market share.

The cigarette industry contributes more than 60 billion Egyptian pounds ($3.8 billion) to government coffers yearly, according tobacco firms.

Under the new terms, sent to tobacco companies on June 1, the winning bidder should agree to produce 1 billion cigarettes per year instead of 15 billion per year.

Authorities also scrapped a rule saying they would not be offering any other licenses after the tender for a decade, the updated document from Egypt's Industrial Development Authority showed.

The deadline to submit offers in the amended tender is Aug. 1.

In March, the Industrial Development Authority invited companies to bid for a licence. Four firms - Nakhla Tobacco Co, Imperial Tobacco, British American Tobacco and Al-Mansour International Distribution Co - complained that the winner would have an unfair advantage over its competitors. Shortly afterwards, the tender was postponed.

(Writing by Nadine Awadalla; Editing by Jan Harvey and Bill Berkrot)