BEIJING (Reuters) - The United States hopes that tentative diplomatic engagement between China and Japan amid their dispute over a group of islands in the East China Sea is successful as escalation is in nobody's interest, a senior U.S. diplomat said on Saturday.

Ties between the world's second- and third-biggest economies have been strained over the uninhabited islets, controlled by Japan but claimed by both countries. The isles are known as the Senkaku in Japan and the Diaoyu in China.

Aircraft and ships from the two countries have played cat-and-mouse in the vicinity of the islands, raising fears of conflict, perhaps sparked by an accident.

Speaking after a tour of the region, U.S. Assistant Secretary of State for East Asian and Pacific Affairs Daniel Russel said the world did not want the spat to get out of hand.

Global interest in economic stability, Russel told a news conference in Beijing, was "too strong for the world's second and third-largest economies to remain at odds.

"We hope that leaders on all sides will exercise restraint and sensitivity and will consistently pursue diplomatic and friendly moves to manage disputes or resolve outstanding issues," he said.

"It is of great concern to the U.S., as it is to all countries that rely on maritime corridors, that there is any risk of an incident that could lead to a crisis or lead to an escalation," he said.

"We hope that quiet diplomatic engagement between Japan and China bears fruit, and we note with interest that Prime Minister Abe and President Xi Jinping had some form of encounter or conversation in St. Petersburg," Russel added, referring to the brief meeting on the sidelines of the G20 summit earlier this month.

Japanese Prime Minister Shinzo Abe is keen to improve ties and has called for dialogue with China, though he has rejected any conditions on talks.

China has shown no inclination to respond to the overtures, aside from the short exchange between the leaders in Russia, and says it has indisputable sovereignty over the islands.

China's military told the United States this week not to support Japan, nor let it do as it pleased, over the islets.

China has long harbored suspicions about U.S. interest in the dispute as the U.S.-Japan security treaty commits the United States to intervene in defense of Japan if there is an attack on Japanese-administered territory.

The United States also has a hefty military presence in Japan, including on the southern island of Okinawa, which is close to the disputed isles.

(Reporting by Ben Blanchard; Editing by Ron Popeski)