By Andrea Shalal-Esa

WASHINGTON (Reuters) - The Air Force met last week with the chief executives of Boeing Co (BA.N: Quote, Profile, Research) and Northrop Grumman Corp (NOC.N: Quote, Profile, Research) to voice concern about the "vitriolic" tone of public statements over a $35 billion refueling aircraft program, two sources briefed about the meeting said on Monday.

The Air Force surprised the industry by awarding the contract for new aerial tankers to Northrop and its European subcontractor, EADS (EAD.PA: Quote, Profile, Research). The decision has sparked howls of protest from Boeing and its supporters in Congress.

Boeing Chief Executive Jim McNerney and Northrop Chief Executive Ron Sugar met on Friday with Gen. Duncan McNabb, the Air Force vice chief of staff since September, said the sources, who asked not to be named.

"There is a lot of unhappiness about how vitriolic the debate has become," said one of the sources. He characterized the meeting as "polite."

Prior to McNabb's current job, he headed Air Mobility Command, the part of the Air Force that provides airlift and aerial refueling for all of the U.S. armed forces.

Boeing has protested the Feb. 29 contract award with the nonpartisan Government Accountability Office, accusing the Air Force of steering the contract to Northrop. Boeing's backers in Congress have vowed to halt funding for the deal if the appeal fails.

Boeing has also run a series of full-page advertisements in U.S. newspapers condemning the Air Force's handling of the deal as "flawed by countless irregularities."

"It's really gotten ugly," said one Air Force official who spoke on condition he not be identified.