Shane Bauer and Sarah Shourd, two of the three Americans held in Iran on suspicion of spying, have got engaged to each other in Tehran's Evin jail and will marry once they are released, their mothers said today.

Bauer, Shourd and Josh Fattal have been jailed since their arrest in July 2009 along Iran's border with Iraq. Their families say the three were hiking in Iraq and strayed over the border accidentally. Iran accuses them of being spies.

Bauer, 27, proposed to Shourd, 31, using an improvised ring he wove together with threads from his shirt, the mothers said in a joint statement. The mothers travelled to Iran last week to visit their adult children for the first time since their arrest.

Fattal, 27, will serve as best man at the wedding, the mothers said.

"Shane told me that he proposed to Sarah in the yard of Evin prison on 6 January, the very same day that we applied for our visas to go visit them," Cindy Hickey, Bauer's mother, said in the statement.

"We're all so overjoyed at the news but it's obviously impossible to know when the wedding will take place. We just hope and pray that Iran will do the right thing and release them so they can get on with their lives," she added.

Iran's intelligence minister, Heydar Moslehi, said on Sunday he had no doubt the three were spies and called on the US to propose a prisoner swap to secure their release, the semi-official Fars news agency reported.

Their imprisonment has further complicated relations between the US and Iran over the latter's nuclear ambitions. US officials have called the three "innocent tourists" and demanded their release but have said they are not considering any kind of prisoner swap.

The mothers told ABC's Good Morning America programme today it was an enormous relief to see their children but that the three had not been told anything about the status of charges against them.

"They are very unaware of anything going on with their case," Hickey said on the show.

The women used last week's visit to plead with the Iranian government to release their children, but they told ABC they did not meet with high-ranking officials, only low-ranking handlers.

The three Americans appeared generally healthy, the mothers said. Bauer and Fattal share a cell, the mothers said. Shourd is being held alone, but is able to see the others twice a day for 30 minutes, they added.