The attacks come as Iraqi forces battle IS in the northern city of Mosul, the last major population centre the jihadists hold in the country.
IS has carried out a series of attacks in other areas since the operation to retake Mosul was launched on October 17 in an apparent bid to draw attention and possibly troops away from the city.
Masum al-Tamimi, a member of the Karbala provincial council, said six suicide bombers armed with light weapons as well as explosives tried to infiltrate Ain al-Tamer early today.
The attack also wounded at least six people, officials said.
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The interior ministry said security forces killed five of the bombers while the sixth detonated explosives inside a house.
But IS issued a statement claiming the attack in which it said that there were only five bombers, identified with noms de guerre indicating two were from Mosul and three from Syria.
The jihadist group said the bombers, who were armed with automatic weapons and grenades as well as explosive belts, battled security forces until running out of ammunition and then blew themselves up.
But Ain al-Tamer, which is located 50 kilometres (30 miles) from the Shiite shrine city of Karbala, is on the edge of Anbar province, which has long been a haven for jihadists.
A similar attack involving militants armed with explosives, rifles and grenades hit Ain al-Tamer in late August, killing 18 people and wounding at least 26.
Later in the day, two more bombers detonated explosives-rigged vehicles near police checkpoints in Fallujah, killing seven people and wounding 25, a police captain and a hospital official said.
"These two explosions are the first two explosions in Fallujah since its liberation from (IS)," Raja Barakat, a member of the provincial council security committee in Anbar province, where Fallujah is located.
The jihadist group overran large areas north and west of Baghdad in 2014, but Iraqi forces backed by US-led air strikes have since regained much of the territory they lost to IS two years ago.