UPDATE 1-Fiat holds share as Italy May car sales fall-CEO

(adds comments on United States)

MILAN, May 20 (Reuters) - Italy's car sales are down again in May after April's 2.86 percent fall, but Fiat (FIA.MI: Quote, Profile, Research, Stock Buzz) kept its market share, the domestic car maker's chief executive, Sergio Marchionne, said on the sidelines of a conference.

"The Italian car market in May continued to show a structural weakness," he said.

"We are down but we are working on it, we are maintaining our market share," he added.

Fiat bucked the trend in April, with registrations of its three main brands rising 1.4 percent to give it a market share of 33.6 percent.

Marchionne added the worst seemed to be over in the United States, even though the market had "structural problems".

"I think the worst is over in America. We are waiting for a recovery in the markets in the third and fourth quarters of this year. Let's see if Europe can manage to hook up to that," he said.

(Reporting by Stefano Rebaudo, writing by Jo Winterbottom; editing by Elaine Hardcastle)