BUDAPEST, Oct 7 (Reuters) - Hungarian drugmaker Richter has manufactured enough doses of COVID-19 drug Remdesivir to treat 3,000 patients, spokeswoman Zsuzsa Beke said on Wednesday, amid shortages of the medication in Europe.

The move comes as the European Union is under pressure to expand its limited stocks of the antiviral drug as COVID-19 cases and hospitalisations rise on the continent.

Remdesivir is usually administered to severely ill patients. This week it has also been given to U.S. President Donald Trump after he tested positive for the virus.

Beke said the Hungarian government, which owns a 5.25% stake in Richter, approached the company during the first wave of the pandemic to explore whether Remdesivir could be manufactured locally.

"We have managed to solve the synthesis of the active substance within five months," Beke said. "The request came from the government and they have also financed the development."

Richter has 260 doses ready to be used in hospitals pending the required clinical trial. Beke said once the medicine gets clearance, Richter would be gradually able to provide further doses of the stock it had already manufactured.

As of Wednesday, Hungary had reported 33,114 coronavirus cases with 877 deaths and 9,149 recoveries. Some 656 people are being treated in hospitals.

At 1310 GMT, Richter shares were 1.6% higher at 6,660 forints on the Budapest Stock Exchange, outperforming the blue chip index, which was 0.3% higher.

(Reporting by Gergely Szakacs; Editing by Mark Potter)