The company said that as of April 12, it has delivered 132 million doses of its vaccine globally, including approximately 117 million doses to the United States.
Health officials started using the Moderna jab in Wales last week and had said it would be rolled out across the rest of the United Kingdom in the coming days.
The Greek statement came as the U.S. company began delivering its vaccine to countries across the EU, a few days later than initially planned due to production issues.
Rovi will start manufacturing of the active agents at its plant in Granada, having previously only packaged vaccines that had been produced in Switzerland, it said in a statement.
Vaccine supply has increased significantly in the United States in recent weeks as Johnson & Johnson has begun making millions of doses of its recently authorized shots.
Profits for companies on the STOXX 600 are expected to jump 47.4pc in the first quarter versus beaten-down numbers a year earlier, according to Refinitiv IBES data.
The United Kingdom has vaccinated 31.6 million people with a first dose of a COVID-19 vaccine - and administered 5.5 million second doses. It will shortly have vaccinated half of its total population.
Moderna has supplied 100 million doses of its vaccine to the United States as of March 29. Pfizer/BioNTech and Johnson & Johnson's shots are the other two vaccines approved in the country.
The J&J vaccine has won praise for its single dosage and because it does not need to be frozen -- unlike the shots from Moderna and Pfizer -- making distribution much simpler.
The overall figure was revised down dramatically after the Anglo-Swedish pharma giant AstraZeneca slashed the number it was providing from a contracted 120 million doses.
The decision came two days before Spain was to resume use of the AstraZeneca vaccine after the EU's drug regulator deemed the jab "safe and effective".
The self-ruled democratic island has signed contracts to purchase 10 million AstraZeneca doses, as well as around 5 million doses each from Moderna and the international Covax scheme.
Health authorities added to the cautious optimism Monday when they announced that vaccinated people could meet together in small groups indoors without wearing masks or the need for social distancing.
Though concern has grown over variants of the virus, especially those that appear to spread more easily and render current shots less potent, Fauci sounded a hopeful note on whether another surge was coming.