BRUSSELS — The U.S. President declared the NATO summit a triumph on Tuesday, praising the "love" and "unity" of member states he had opened the week by threatening to abandon, shortly after demanding the alliance hand over Greenland.

Greenland remained Danish. Member states, for their part, agreed to raise military spending by 20 percent and to credit the increase to the President's negotiating skill. "The most reliable way to preserve the alliance is to praise his intelligence and quietly keep our own territory," said a senior European official, reported to be the favourite for the alliance's top job after managing the President's temperament through the closed sessions.

The pattern was familiar. An earlier cycle had seen the same threats to the post-war order dissolve once members offered spending increases and sufficient personal validation, and this summit resolved on the same terms, with the President accepting credit for budget rises that governments had already planned.

"The alliance has never been more unified," a spokesman said of the lasting erosion of transatlantic trust, from a podium set in front of a map on which Greenland was still coloured Danish.