CAIRO, Sept 3 (Reuters) - UAE's Global Investment Holding Co. has agreed to buy a 30% stake in Eastern Co. , Egypt's main tobacco products maker, for $625 million, a measure that will widen private participation in the economy, Egypt's cabinet said on Sunday.

Last month, Egypt state-owned Holding Company for Chemical Industries, which held 50.95% of Eastern's shares, said in a stock market disclosure it had received offers from foreign investors to buy up to half of its shares.

The sale will reduce Chemical Industries' stake to 20.95%, giving impetus to Egypt's floundering privatisation programme.

Global Investment will provide $150 million to buy the tobacco necessary for production as part of the agreement. It was not clear from the statement if this was an additional amount or was included in the $625 million purchase price.

Egyptian Prime Minister Mostafa Madbouly and the finance and public enterprise ministers attended a signing ceremony for the purchase.

The deal "is an affirmation of the government's determination to ... encourage direct private investment in various sectors," the cabinet statement said.

Egypt's government sold 4.5% of Eastern Co. on the stock exchange in 2019, leaving the holding company with a majority stake.

Egypt promised the International Monetary Fund it would roll back the state's involvement in the economy and allow private companies a much greater role as part of a $3 billion, 46-month financial support package signed in December.

The IMF's first review of the Extended Fund Facility, initially scheduled for around March, has yet to take place, partly the result of Egypt's slow progress on asset sales.

Since then, a number of sales to foreign investors had been announced in principle, but few have been completed.

Egypt desperately needs foreign currency after the COVID pandemic and Ukraine crisis exposed vulnerabilities in its economy. The government is facing an increasingly tough repayment schedule after a borrowing spree over the past eight years quadrupled its foreign debt.

Eastern's share price has risen by about 11.7% to 20.40 Egyptian pounds ($0.64) since news of the foreign offers was announced on Aug. 22. (Reporting by Momen Saeed Atallah, Writing by Adam Makary, Hatem Maher and Patrick Werr, Editing by Ros Russell)