Violence also continued near the volatile northern city of Mosul, where scores have been killed in bombings this month.
A car bomb struck an Iraqi army patrol in a Sunni village near the Syrian border, killing four soldiers, according to police.
The attacks revealed "breaches and soft areas in our security system," Khalid al-Attiyah, deputy speaker of the parliament, said.
"This matter requires a comprehensive review of the system and finding the shortcomings in order to fix them."
He said recommendations included the creation of a joint committee of officials from the interior, defence and national security ministries to determine how to better investigate and prosecute armed groups.
The officials also called for holding any security leaders found to be negligent responsible, improving the co-ordination between intelligence agencies and tightening control over the release of detainees.
Thousands of detainees in US custody have been freed or transferred into government custody as called for by the security pact.
That has raised concern that many of the detainees, most of them Sunni men, have joined the armed groups upon their release.
"There has been unacceptable tolerance in the treatment and interrogation of the detainees under the pretext of respecting human rights, forgetting the rights of hundreds of innocent victims," al-Attiyah said.
He also called for amending an amnesty law that led to the release of prisoners not convicted of major crimes in a bid to foster reconciliation between Sunnis and Shia.