A court in Tehran has issued the first death sentence to a person arrested for taking part in protests.
A human rights group warned authorities might be planning "hasty executions".
At least 20 people are currently facing charges punishable by death, Norway-based Iran Human Rights said, citing official reports.
Its director, Mahmood Amiry-Moghaddam, called on the international community to take urgent action and "strongly warn the Islamic Republic of the consequences of executing protesters".
The execution was ordered for an unidentified person for allegedly setting fire to a government building. It followed 272 of Iran’s 290 lawmakers voting earlier this month to implement the death penalty for serious crimes against the state.
The court in Tehran found the defendant, who was not named, had set fire to a government facility and was guilty of "enmity against God".
Another court jailed five people for between five and 10 years on national security and public order charges.
Upwards of 326 people have died in 57 days of demonstrations, which erupted after the death of a young woman who was detained for wearing her headdress “inappropriately”. Thousands more have been detained.
Iran's leaders have portrayed the protests as "riots" instigated by the country's foreign enemies.
Last week, judiciary chief Gholamhossein Mohseni Ejei declared that "key perpetrators" should be identified as soon as possible and handed sentences that would have a deterrent effect on others.
Read more at the BBC