By Jon Herskovitz

AUSTIN, Texas (Reuters) - China has set a Sept. 19 trial date for a U.S. businesswoman accused of spying, charges her husband in Texas said on Thursday were false, and the U.S. State Department said it was concerned about her welfare.

Sandy Phan-Gillis, who was born in Vietnam and has Chinese ancestry, was arrested on suspicion of spying by Chinese authorities in March 2015 while visiting the country as part of a trade delegation from Houston.

In a statement on Thursday, her husband Jeff Gillis accused Chinese authorities of suppressing evidence that would weaken the case against her. "The charges are absolutely false," he said, adding that he wants U.S. President Barack Obama to ask for her release when he attends a summit with China's leader this week.

The announcement of a trial date renewed attention on her case just ahead of a visit to China by Obama, who is due to arrive on Saturday for a G20 summit in the city of Hangzhou. Obama is scheduled to hold bilateral meetings with Chinese President Xi Jinping on Saturday.

Gillis said a main contention of the charge against his wife was that she had gone on a spy mission to China in 1996.

He said her U.S. passport showed she had not traveled to China at that time and accused the Chinese Consulate in Houston of refusing to acknowledge that there were no entry or exit visas from China in that passport. This, he said, prevented her passport from being used as evidence at her trial.

The Chinese Embassy in Washington and the Chinese Consulate in Houston did not respond to requests for comment.

Beijing officials said this week that Phan-Gillis, now a U.S. citizen, had been formally charged with spying.

"We continue to monitor her case closely," State Department spokesman John Kirby said at a press briefing in Washington, adding that officers from the U.S. consulate Beijing had visited her on a monthly basis since she was detained.

"We have repeatedly pressed Chinese authorities to provide further details of the case and to give our consular officers full and unrestricted access to her as required by the Vienna convention. We urge the government of China to review and consider seriously the ... views expressed by the U.N. working group on arbitrary detention, including its recommendation to release Ms. Phan-Gillis."

At a regular briefing this week in Beijing, Chinese Foreign Ministry spokeswoman Hua Chunying told reporters, "Based on our understanding, Phan-Gillis, because of her suspected crimes of espionage, has been charged according to law by the relevant Chinese department."

(Additional reporting by Arshad Mohammed in Washington; Editing by Alan Crosby and James Dalgleish)