Iraq's Kurds said Thursday Prime Minister Nuri al-Maliki was "hysterical" and not fit to run the country, further dimming the prospect of a new leadership uniting to face jihadist fighters.

The worsening political discord comes three days ahead of a planned parliamentary session meant to revive the process of replacing what has effectively been a caretaker government since April elections.

Maliki "has become hysterical and has lost his balance", a statement from the office of Kurdish regional president Massud Barzani said, reacting to accusations by the prime minister a day earlier that his administration was harbouring militants.

Kurdish troops moved into disputed areas vacated by federal forces that failed to stop a Sunni militant onslaught that began on June 9.

The Kurds have since said those swathes of land were theirs to keep, and announced plans to hold a referendum on independence.

Maliki has accused Barzani of exploiting the chaos created by the Islamic State (IS) jihadist group's military offensive, but the Kurdish president said the security collapse was of the premier's own making.

"You must apologise to the Iraqi people and step down. You have destroyed the country and someone who has destroyed the country cannot save the country from crises," the statement said.

- Fallujah air strikes -

Since IS leader Abu Bakr al-Baghdadi proclaimed a "caliphate" twice the size of Israel on land straddling Iraq and Syria, militants have not made any further significant advances.

But Iraqi forces have also struggled to reclaim lost ground, and the front lines north and west of Baghdad are increasingly looking like the de facto borders of a partitioned Iraq.

Despite backing in the shape of hardware, manpower and intelligence from sources as diverse as Iran, Iraqi Shiite militias and the United States, the government has so far failed to recapture Tikrit, the home town of executed former president Saddam Hussein.

And it is far from being able to even attempt retaking Mosul, a city of two million further north and the setting for a video posted online last week purporting to show Baghdadi delivering a Ramadan sermon, a stunt analysts said showed huge confidence on the part of IS.

A Sukhoi jet of the kind recently delivered by Moscow, and apparently Tehran, attacked a market Wednesday in the rebel-held city of Fallujah, which lies only 60 kilometres (35 miles) west of the capital.

According to doctor Ahmed Shami, eight people were killed and 35 wounded. He said five children were among another 12 wounded in further air strikes on Thursday.

- Dilatory tactics -

The escalating war of words between Maliki and the Kurds has already cast a pall over a key parliament session slated for July 13.

In a sign of what may be to come in parliament, Kurdish ministers said Maliki's stance "only served the enemies of Iraq and the terrorists" and announced they were boycotting cabinet sessions.

The new Iraqi MPs' first attempt at selecting a speaker, president and government on July 1 ended in disarray, with deputies trading threats and heckles and some eventually walking out.

The next session was announced for August 12 but the timing caused an outcry, with both regular Iraqis and the international community exasperated by the lack of urgency their politicians were displaying with the country was mired in its worst crisis in years.

While many of Iraq's factions, apparently including some within the prime minister's own bloc, agree that Maliki needs to step aside if deadly sectarianism is to be reined in, the incumbent has insisted his poll victory legitimised his bid for a third term.

Some observers argue Maliki is intentionally seeking to scupper the upcoming parliament vote to buy more time and tip political support back in his favour.

"He's trying to play it long because it's his only chance," one Western diplomat told AFP on condition of anonymity.