"I appealed the verdict yesterday (Saturday) and it is up to the judges in the appeals court to review the case," Masoud Shaffi said, adding that the appeals procedure could be very quick or take several months "according to the judges."
"I believe that my clients are innocent so if the appeals judges look at the case within a legal framework, and show compassion because we are in the month of Ramadan," the pair could be freed before the end of the holy fasting month, he said.
Ramadan should be over by the middle of next week.
The two hikers, Shane Bauer and Josh Fattal, were sentenced to eight years in jail each on charges of espionage and illegal entry, Tehran prosecutor Abbas Jafari Dolatabadi said earlier this month.
The verdict triggered "deep disappointment" in Washington which insists that the two men are innocent.
"The case of Sarah Shourd who has been freed on bail is still open," Jafari Dolatabadi said last week, referring to a third American who was arrested along with her fiance Bauer and Fattal on July 31, 2009.
She was freed on bail of around 500,000 dollars and returned to the United States in September on humanitarian and medical grounds.
The relatives of the two men urged the Iranian government to show "compassion" and free them upon finding about the verdict.
The trio were arrested on the unmarked border between Iran and Iraq, claiming they were hiking in Iraq's northern province of Kurdistan when they innocently strayed into the Islamic republic.
They pleaded not guilty to spying charges, according to their lawyer.
Shourd, a teacher, writer and women's rights activist, met Bauer, a fluent Arabic-speaking freelance journalist, while helping to organise demonstrations in the US against the war in Iraq. The two moved to Damascus together in 2008.
Fattal, who grew up in Pennsylvania, is an environmentalist and teacher. He travelled in 2009 to Damascus, where he met Shourd and Bauer.