"What you received on Tuesday is... the first stage that, God willing, will be followed by revenge for those whom you executed," the statement said.
At least 20 explosions and multiple shootings hit Iraq on Tuesday, many of them in Shiite neighbourhoods of Baghdad during morning rush hour.
The statement called the attacks a "quick response" to the Iraqi justice minister, who said on Monday that "nothing" would stop Iraq from carrying out controversial executions.
Iraq put at least 129 people to death last year and carried out several mass executions, including one in which 21 people were executed in a single day.
The executions sparked calls for a moratorium from the UN mission in Iraq, as well as from Britain, the European Union and rights groups Amnesty International and Human Rights Watch.
Violence in Iraq has fallen from its peak in 2006 and 2007, but attacks remain common, killing 220 people in February, according to an AFP tally based on security and medical sources.