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By John Irish

NEW YORK, Sept 20 (Reuters) - French President Emmanuel Macron said on Wednesday the Iran nuclear deal was not enough given that Tehran had increased its influence in the region and pressed ahead with ballistic missile tests, and offered to mediate between the United States and Iran.

Macron, whose country had been one of the toughest negotiators during the talks between Britain, China, Germany Russia, United States and Iran, repeated that it would be an error to scrap the deal.

"Is this agreement enough? No. It is not, given the evolution of the regional situation and increasing pressure that Iran is exerting on the region, and given increased activity by Iran on the ballistic level since the accord," Macron told reporters in New York.

Macron said he wanted to discuss possible sanctions over Iran's ballistic missile programme, open negotiations immediately on what happens after the limitations to the accord begin to be lifted in 2025 and hold a discussion on the role of Iran in the region.

"Let's be honest, the tensions are on the rise, look at the activities of Hezbollah and Iran's pressure on Syria. We need a clear framework to be able to reassure regional countries and the United States," Macron said, adding that he was ready to mediate between the United States and Iran.

Macron said he had not given up on convincing U.S. President Donald Trump, who has called the deal "the worst ever", to change his mind.

The French leader said he believed he had managed to at least convince Trump to allow France and the United Nations to play a mediation role between Tehran and Washington with regard to the situation in Syria, where Iran is a core backer of Syrian President Bashar al-Assad.

SYRIA TALKS

"I proposed that we initiate the work of a contact group at P5 level (Britain, China, Germany, France, Russia), which has been done and we will widen it to represent the political forces in Syria and the regional powers without Iran," Macron said.

"The United Nations Secretary General and France will play the role of mediator for Iran so that we have a parallel negotiation, but that will enable us to include Iran in the process," he said.

The foreign ministers of the P5 will meet to discuss the group Thursday morning at the U.N., where leaders are gathered for the world body's annual general assembly.

The last major international attempt to resolve the crisis ended in failure when the International Syria Support Group (ISSG), which included Iran, was cast aside after Syrian government forces retook the rebel stronghold of Aleppo in 2016.