The session opened with 297 of 328 MPs in attendance, according to parliament speaker Salim al-Juburi.
Abadi on Sunday proposed a series of measures aimed at curbing corruption, streamlining the government and improving services after protests and a call from Iraq's top Shia cleric Grand Ayatollah Ali al-Sistani for drastic change.
Juburi has urged MPs to sign off on the reforms proposed by Abadi, which have already been approved by the cabinet, but said that more measures are needed.
Amid a major heatwave that has seen temperatures top 50 degrees Celsius (120 degrees Fahrenheit), protesters have railed against the poor quality of services, especially power outages that leave just a few hours of government-supplied electricity per day.