LONDON (Reuters) - Tensions around Georgia's controversial draft "foreign agents" law could hit the country's economy and investor confidence, the president of the European Bank for Reconstruction and Development (EBRD) warned on Tuesday.

The draft legislation, which is winding its way through the Georgian parliament, would require organisations receiving more than 20% of their funding from abroad to register as agents of foreign influence, a requirement opponents attack as authoritarian and Kremlin-inspired.

The draft legislation sparked protests in recent days while Brussels and Washington have urged Tbilisi to drop the legislation or risk harming its chances of European Union membership and a broader Euro-Atlantic future.

"We were surprised to see it coming back, and we are concerned by the dynamics of what's involved," EBRD President Odile Renaud-Basso told journalists during a media briefing ahead of the lender's annual meetings kicking off in Armenia on May 14.

Georgia has benefited economically from making good reform progress, Renaud-Basso said.

"But the new trend and the tension around that (draft law) could have an impact, an economic impact, on the private sector and the willingness to invest in the country so we are in contact with our partners," she said.

(Reporting by Libby George, editing by Karin Strohecker)