Shane Bauer and Josh Fattal, both 29, were arrested along with Sarah Shourd, 32, on the unmarked border between Iran and Iraq on July 31, 2009.
Iran accuses the three of "spying and illegally entering the country."
They have pleaded not guilty to spying charges, saying they were hiking in Iraq's northern province of Kurdistan when they innocently walked into Iran across an unmarked border.
Washington has vehemently denied Tehran's charges and has pressed for their release.
Shourd, who got engaged with Bauer while in prison in Tehran, is being tried in absentia after she returned to the United States following her release on humanitarian and medical grounds in September 2010, for which bail of about 500,000 dollars was paid.
"Since the hearing date coincides with the two year anniversary of their arrest, and it is the beginning of the holy month of Ramadan, I am hopeful that this case has a happy ending," their lawyer Masoud Shafii told AFP on Wednesday referring to the Muslim fasting month when compassion, the spirit of caring and sharing is advocated.
"I believe that they are innocent; the espionage charges have no relevance. Even if the court does not accept my defence, the two years they've spent behind bars is punishment enough," he added referring to the illegal entry charge.
Ahead of the new hearing their families issued a statement on Friday in New York, and Shourd used her statement to wish Muslims in Iran and everywhere a blessed Ramadan on behalf of the families of the two men.
"Please, if you could make a little room in your prayers on the eve of Ramadan for my fiance, my friend and our families, it would mean the world to us," she said.
The trial has been hit by a number of delays since November 6, 2010, when it was postponed to February 6, 2011 over what was termed "an error in the judicial proceedings."
Another hearing scheduled for May 11 this year was cancelled after Fattal and Bauer were not brought before the court, according to Shafii.
Shourd, who did not attend the February 6 hearing, told AFP in Washington that she will not return to Iran to join the other two in the dock.
She said she had sent Iran's revolutionary court a five-page evaluation by a clinical forensic psychologist, who concluded she was at high risk of psychological problems if she returned to face espionage charges.
Shafii said he has met Bauer and Fattal only twice, the last time on February 6, 2011 when they appeared in court for the first hearing.
"I still have not met them (for) the lawyer-client meeting that I have requested. They told me that they will inform me and I am still pursuing it," he said.
Their case has attracted high profile support in the United States.
On May 24, the legendary Muslim boxing champion Muhammad Ali supported a call for Iran's supreme leader Ayatollah Ali Khamenei to free Bauer and Fattal.
Amnesty International on Friday renewed calls for Iran to release the two hikers.
The hikers' detention has added to the animosity between arch-foes Tehran and Washington, which has increased over Iran's disputed nuclear drive and outspoken remarks by hardline President Mahmoud Ahmadinejad