By Jeffrey Dastin

(Reuters) - United Continental Holdings Inc <UAL.N> and its flight attendants have agreed to extend mediated contract talks this month after scheduled discussions ended last week without a deal for unified work rules and benefits, they said on Monday.

U.S. federal mediators directed the parties to resolve contract language issues next week ahead of a new final mediation session during the week of June 20, the Association of Flight Attendants-CWA said in an online notice. United said in a separate online bulletin that it was "committed to bringing this negotiation to a successful close."

Flight attendants from United and Continental Airlines, which merged in 2010, still staff separate flights and operate under different work rules. Furloughs by the merged company's previous management strained labor relations, and the parties entered federal mediation in November 2015.

A single contract for all flight attendants would mark an achievement for new Chief Executive Oscar Munoz. His appointment in September led to a "marked improvement" at the negotiating table, the union said. He has stressed that employees are integral to improving customer satisfaction scores that have lagged those of its peers.

The union has called on members to picket United's annual shareholder meeting on Wednesday in Chicago, the latest monthly protest to draw attention to their contract.

(Reporting by Jeffrey Dastin in New York; Editing by Richard Chang)