According to the reports authorities are trying to bring the wave of unrest under control while political leaders were to meet Saturday for talks on persistent disputes that have paralyzed the government.
Figures for the May death toll ranged from more than 600, according to the government, to more than 1,000, according to the United Nations.
Either would make the violence the deadliest since 2008.
Available data from the Iraqi government ministries put the toll at 681 dead and 1,097 wounded. The UN gave a significantly higher toll of 1,045 killed and 2,397 wounded.
The figures were released ahead of a meeting of leading politicians including Prime Minister Nuri al-Maliki and several of key officials planned for later Saturday.
The long-discussed meeting is aimed at resolving a wide variety of disputes between the country's political blocs, some of which have persisted for several years.
UN envoy Martin Kobler warned on Thursday that "systemic violence is ready to explode at any moment".
Maliki has warned of attempts to return Iraq to "sectarian civil war". He called on everyone worried about Iraq's future "to take the initiative, and not be silent about those who want to take the country back to sectarian civil war."
The current violence in the county, he said, “is an intrigue plotted for Iraq, so we call on the politicians to confront this plot by consolidating brotherhood among them and avoid harming their country.”