Story highlights ISIS says bombers from Libya and Lebanon

Two attacks kill more than 20

Iraqi Parliament reportedly won't meet until August

Iraq close to finishing investigation into video purportedly of ISIS leader

The Islamic State in Iraq and Syria has claimed responsibility for recent suicide bombings in the capital that killed nearly two dozen people, according to SITE Intelligence, which monitors terrorist groups.

ISIS identified the suicide bombers who struck Baghdad on Sunday and Monday as Libyan and Lebanese, SITE reported, citing a website linked to the terror group.

One of the bombings occurred Sunday in the Washash district of Baghdad, when a suicide bomber struck a coffee shop, killing at least a dozen people, security officials told CNN.

The second occurred Monday in the Kadhimiya neighborhood, security officials told CNN. A suicide car bomb exploded in heavy traffic at a security checkpoint there, killing at least 10 people and wounding 14, security officials told CNN.

The bomb exploded at about 1 p.m. near the checkpoint, which created a sort of bottleneck of traffic. The explosion occurred about 1 kilometer (.6 miles) from the Kadhimiya shrine, which is revered by Shiites.

Parliament session put off

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Just hours after the caretaker speaker of Iraq's Parliament called on lawmakers to return Sunday to try to form a new government, state-run Iraqiya TV reported it had been postponed for another month.

"I invite the parliamentary blocs in this period to approve the necessary nominations in order to start the parliamentary session and the formation of the government," Speaker Mehdi al-Hafez said in a written statement provided to CNN.

"The delay in that will put Iraq's security and its move towards democracy at risk. Also it will increase the suffering of the Iraqi people, and it will encroach on the rights of voters."

Citing sources in Parliament, Iraqiya reported that the session was postponed until August 12 because the political parties have been unable to reach a consensus on who to name to top leadership posts. Those include the speaker, the president and the prime minister.

A week ago, Iraq's Parliament postponed its first session, citing a lack of a quorum after 90 of the 328 lawmakers walked out.

Al-Baghdadi investigation to be released

Iraq plans Wednesday to release its findings of its investigation into whether a man featured in a video delivering a sermon in Mosul is notorious ISIS leader Abu Bakr al-Baghdadi, military spokesman Qassim Atta told reporters.

Those findings are expected to include details about al-Baghdadi's movement, Atta said.

The video surfaced on social media sites tied to ISIS, the terror group that now calls itself the Islamic State. It shows a man identified as al-Baghdadi conducting Friday prayers at the Great Mosque of al-Nuri.

If it is al-Baghdadi, it would be one of the first known appearances of the elusive extremist militant leader to be captured on video. Very few images have been made public of al-Baghdadi.

His appearance comes days after ISIS declared him as the leader of its new "caliphate," or Islamic state, extending from Aleppo in northeastern Syria to the Diyala province in Iraq.