DUBAI, July 28 (Reuters) - Iran should free Washington Post journalist Jason Rezaian because there was no evidence to support charges, including spying, made against him, the Iranian-American reporter's lawyer was quoted by Iran's Tasnim news agency as saying on Tuesday.

Leila Ahsan, told Tasnim in May that her client had been charged with espionage for collecting confidential information, handing it to hostile governments, writing a letter to U.S. President Barack Obama, and acting against national security.

The first hearing in the trial was in May, some 10 months after the newspaper's Tehran bureau chief was detained.

"I have reviewed my client's case and there is no evidences or documentation to prove he has committed the crimes," Tasnim quoted Ahsan as saying.

"Under the conditions imposed by the Vienna deal, we have called for an immediate acquittal of my client."

The United States, France, Russia, China, Britain and Germany ended a years-long standoff with Tehran on July 14 in Vienna by reaching a deal with Iran on its nuclear work.

Rezaian's wife Yeganeh Salehi and a woman photojournalist were detained with him were released on bail but also went on trial in May, Iranian media reported.

Rights groups, Obama and relatives have all called for Rezaian's immediate release. Washington has rejected the "absurd" espionage charges against him.

"He has been jailed over a year and ... keeping him in jail is illegal based on Iran's new penal code," Ahsan said.

Iran's new penal code bars those on trial for charges other than murder from being in detention for more than a year before a verdict, Tasnim said.

Rezaian, held at Tehran's Evin prison, could be sentenced to up to 20 years in jail if convicted, Iranian media reported. U.S. officials, the Washington Post and rights groups have repeatedly criticised Rezaian's trial.

Ahsan said that the next hearing could be the final one but she had not been told on what date that session would be.

(Editing by Louise Ireland)