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LONDON, June 22 (Reuters) - Britain's Middle East minister Andrew Murrison will visit Iran on Sunday for "frank and constructive" talks, the Foreign Office said, amid escalating tension between Tehran and Washington after the downing of an unmanned U.S. drone.

U.S. President Donald Trump said on Friday he aborted a military strike to retaliate for the drone incident because it could have killed 150 people, and signaled he was open to talks with Tehran.

Iran responded on Saturday by saying it would respond firmly to any threat against it, the semi-official Tasnim news agency reported.

"At this time of increased regional tensions and at a crucial period for the future of the nuclear deal, this visit is an opportunity for further open, frank and constructive engagement with the government of Iran," the Foreign Office said in a statement.

Murrison, a junior minister in the Foreign Office, will call for urgent de-escalation in the region and raise concerns about "Iran's regional conduct and its threat to cease complying with the nuclear deal to which the UK remains fully committed," the statement said.

Britain is one of six foreign signatories to the 2015 deal with Iran in which the Islamic Republic agreed to suspend its nuclear programme in return for a lifting of economic sanctions.

But Trump pulled the United States out of that deal and reimposed sanctions on Tehran. The three European signatories, which also include Germany and France, have been trying along with Russia and China to salvage the deal.

Iran has said it will not give the European powers more time beyond July 8 to save the nuclear deal. It has said it is ready to go through with a threat to enrich uranium to a higher level if Europe cannot shield Tehran from the U.S. sanctions. (Reporting by Alistair Smout; editing by John Stonestreet and Gareth Jones)