On Thursday, Iraqi Prime Minister Haider al-Abadi ordered the “immediate application” of death sentences against convicted terrorists.
A day earlier the bodies of eight captives held by the Islamic State group (IS) were found on a road north of the capital Baghdad.
Human rights groups have raised serious concerns about trials of IS suspects and mass executions.
At least several hundred people, including foreigners, are believed to be on death row for terrorism in Iraq.
“Based on the orders of Prime Minister Dr Haider al-Abadi, death sentences were carried out on Thursday against 12 convicted terrorists who had received their final sentences,” a message on the prime minister’s Facebook page read.
A Ministry of Justice statement said that 13 people had been executed.
The Iraqi government has not released the identities of those sentenced to death.
Although Mr Abadi announced the end of operations against IS in December, the jihadist group continues to carry out guerrilla-style attacks in parts of the country.
Thousands of people have been arrested in recent years on suspicion of belonging to IS, with an unknown number facing execution.
‘Due process failure’
Around 700 foreign women have either been charged or are awaiting trial, with one German woman sentenced to death in January.
Rights groups have said they are very worried about the way in which trials against IS suspects have been conducted and about the carrying out of several mass executions.
Belkis Wille, a senior Iraq researcher at Human Rights Watch (HRW) who has followed trials in Nineveh Governorate, said that – owing to Iraq’s slow-moving justice system – it is unlikely that any of the 12 who were executed had been convicted recently.
She said that anti-terrorism trials across Iraq “fundamentally fail to provide basic levels of due process”, with many cases relying solely on defendants’ confessions without guarantees that torture was not used.
Last year, Iraq had the fourth highest number of executions in the world, after China, Iran and Saudi Arabia, according to Amnesty International.