Iraq's presidency said a session of parliament would be held on July 1, the first step to forming a new government that the international community hopes will be inclusive enough to undermine the insurgency.
The overnight offensive included Mansouriyat al Jabal, home to the gas fields where foreign companies operate, security forces said. The fighting threatens to rupture the country two and a half years after the end of US occupation.
The insurgents, led by the hardline Islamic State in Iraq and the Levant (Isis) but also including other Sunni groups, blame Prime Minister Nuri al Maliki for marginalising their sect during eight years in power, and he is fighting for his job.
Three months after elections, a chorus of Iraqi and international voices have called for the government formation process to be started, including Iraqi's most influential Shi'ite, Grand Ayatollah Ali al Sistani.
The presidency issued a decree yesterday for the parliament session on Tuesday. Parliament will then have 30 days to name a president and 15 days after that to name a prime minister, although the process has been delayed in the past, taking nine months to seat the government in 2010.
Mr Maliki has dismissed the call of mainly Sunni political and religious figures for a "national salvation government" that would choose figures to lead the country and, in effect, bypass the election.