Iraq said Saturday foreign military trainers who will aid its fight against jihadists are welcome but "late", as a wave of car bombs killed dozens, highlighting enormous security challenges ahead.

US President Barack Obama unveiled plans the day before to send up to 1,500 additional US military personnel to Iraq, which would roughly double the number of American troops in the country.

The move marked a deepening US commitment in the open-ended war against the Islamic State (IS) jihadist group, which spearheaded a June offensive that overran significant parts of Iraq and also holds territory in neighbouring Syria.

A US-led coalition is carrying out a campaign of air strikes against IS in both Iraq and Syria, and countries including Britain, France and Germany have also deployed advisers and trainers to Iraq, which is struggling to repel the jihadists.

"This step is a little late, but we welcome it," a statement from Prime Minister Haidar al-Abadi's office said.

The government had requested that members of the international coalition battling IS help train and arm its forces, the statement said.

"The coalition agreed on that and four to five Iraqi training camps were selected, and building on that, they have now begun sending the trainers," it said.

Multiple divisions collapsed in northern Iraq in the early days of the jihadist offensive, leaving major units that need to be reconstituted.

Experts say Iraqi security forces suffer from serious shortcomings in training and logistics, hampering their performance in the conflict.

Obama had resisted keeping troops in Iraq earlier in his term, vowing to end the American presence that began with the 2003 invasion and lasted until 2011.

Officials had weighed keeping several thousand troops in the country after 2011, but talks with the Iraqi government, then led by prime minister Nuri al-Maliki, broke down over the issue of legal immunity, which Washington insisted on and Baghdad declined to provide.

- Wave of car bombs -

With Friday's announcement, Obama will be deploying a force to Iraq along the lines of that considered in 2011, under legal protections similar to those it rejected as insufficient three years ago.

Iraq has turned to Shiite militias and mainly Sunni tribesmen to bolster its flagging forces, but insisted in its statement on the trainers that arming the latter group is going forward "under the supervision of the Iraqi security forces".

"We will not allow any weapons outside the framework of the state," it said.

But Shiite militias have proliferated and grown much more powerful in the course of the conflict, and it will be difficult for Baghdad to control weapons provided to the country's powerful tribes.

Highlighting the major security challenges the government faces even inside territory it holds, a wave of car bombings struck Shiite-majority areas of Baghdad on Saturday, killing at least 33 people.

The six bombs, in five different areas of the capital, also wounded more than 100 people.

The deadliest single attack was in Sinaa Street in the city's central Karrada district, and killed at least 10.

Two car bombs also hit the Amil area of south Baghdad, and one each exploded in Ameen in the east, Zafraniyah in the centre and Sadr City in the north.

Baghdad is hit by near-daily bombings and shootings, some of which have been claimed by IS, which, like other Sunni extremist groups, considers Shiites heretics and frequently targets them.

In neighbouring Syria, US-led air strikes hit jihadist positions in the north and east, including an oilfield, the Syrian Observatory for Human Rights said on Saturday.

"Four explosions were heard during the night in Deir Ezzor province (eastern Syria), caused by US-Arab air strikes in the area of the Tanak oilfield and an IS checkpoint... killing two people," said the Observatory.

IS controls most oilfields in Deir Ezzor which borders Iraq, and smuggled oil is one of the jihadist group's sources of revenue.