Violence continued across Iraq today as government troops and Kurdish militia proceeded with ongoing efforts to claw back territory lost to hardline Sunni insurgents the Islamic State, and a series of suicide bombings rocked the capital of Baghdad.

Peshmerga fighters from semi-autonomous Iraqi Kurdistan are attempting to retake territory claimed by the Islamic State earlier this month, while the Iraqi military is still attempting to make a meaningful dent on the large swathe of northern Iraq the insurgents overran in June.

The peshmerga, backed by Iraqi air force strikes, took back three villages around Jalawla today, a Kurdish source told AFP, as well as a vital supply road to the town, which takes it a step closer to surrounding the city entirely.

The Kurdish forces initially retreated in the face of the Islamic State's offensive, but are now holding and retaking ground. This is in part thanks to a series of American air strikes on extremist positions from August 8, weapons shipments from the US and others, as well as reinforcements from Kurdish guerrilla groups. Peshmerga also beat off two Islamic State offensives on Tuz Khurmatu and retook Qaraj on Sunday, with the help of Iraqi air strikes.

Meanwhile, at least 20 died in today's Baghdad bombings, with the deadliest attack taking place at a mosque in the eastern New Baghdad district as worshippers left after midday prayer. Police and medical sources told AP that 15 people were killed and 32 others injured.

Three more were reportedly killed and 11 injured when a roadside bomb intended for a police patrol in the southern Dora neighborhood was detonated beside a civilian car. Two more victims died in a bombing at an outdoor market in the north of the capital.

A man walks past blood stains on the floor of the Imam Ali mosque after a suicide bomb attack today in New Baghdad, Iraq. Image via AP/Khalid Mohammed.

The explosions took place after Iraq's new Prime Minister-to be Haider al-Abadi told state TV that a framework for a new administration should be unveiled within 48 hours. Abadi will form a new government intended to represent all of the country's religious groups and help mount a united response against the Islamic State, Reuters reported.

Al-Abadi also used his address to demand that the Iraq's many armed militia groups be brought under government control. "There is no place for armed groups whether from the militias, the tribes or the volunteers... We will not allow the formation of armed groups out of control of the state," he stated.

The militias have had an uneasy and inconsistent relationship with authorities in the past; fighting them at times and cooperating with them at others. However, the rapid advance by the Islamic State, coupled with the spectacular collapse of a significant part of the Iraqi armed forces, meant that lawmakers and military chiefs felt they needed the Shiite gunmen to help defend the capital and granted them more powers and influence as a result. They are now often visible around the city, accompanying police and military patrols.

On Friday, Iraq's leading Shiite cleric, Ayatollah Ali al-Sistani, also issued a call for Iraqis to take up arms against the Islamic State and thousands of volunteers joined militias as a result.

The Islamic State's policy of sectarian attacks and attempts to create outright chaos have spooked Iraq's leaders, and allowed militias to boost their strength and numbers. In some cases, this seems to have been accompanied by a return to the campaign of kidnappings and killings last seen during the brutal sectarian violence that almost tore the country apart in 2006.

Today's attacks came after a bloody weekend, which saw at least 42 dead in attacks in bombings in Baghdad and northern Kirkuk on Saturday. The previous day, 68 were killed and scores wounded in an attack by a suicide bomber and gunmen on a mosque in Diyala province.