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UPDATE 1-EU leaders warn of damage to global growth from trade war

* Juncker says US-China trade war hurting world economy

Tusk says Iran tension a serious concern, urges restraint (Adds quotes, background; paragraph 2 onwards)

By Chris Gallagher and Leika Kihara

OSAKA, June 28 (Reuters) - European Union leaders warned on Friday against the damage that escalating U.S.-China trade friction was inflicting on the global economy, as the Group of 20 economies began a two-day summit in Japan's western city of Osaka.

The annual G20 summit kicked off amid heightened global anxiety over a U.S.-China trade war and escalating tension over Iran's nuclear commitments that threatened to overshadow talks on other issues such as climate and the digital economy.

All eyes are on a high-stakes meeting between Donald Trump and China's President Xi Jinping on the sidelines of the G20 and whether the U.S. president will carry out his threat of additional tariffs on Chinese goods.

"The trade relations between China and the U.S. are difficult, they are contributing to the slowdown of the global economy," European Commission President Jean-Claude Juncker told a news conference.

"In our talks, both with the U.S. and the Chinese authorities ... I was drawing their attention to the harmful impact this controversial matter is creating."

Juncker said the European Union was working closely with China, Japan, the United States and others to reform the World Trade Organization and create a level playing field.

Work to draft the G20 communique continued, he added.

European Council President Donald Tusk expressed concern about Iran potentially breaching its nuclear commitments, saying the European Union would continue to monitor Tehran's compliance.

"We strongly urge Iran to continue the full implementation of all its commitments under the nuclear deal, and we take very seriously the possibility of any breach of its commitment," Tusk told the news conference. (Reporting by Leika Kihara and Chris Gallagher; Editing by Clarence Fernandez)