In their Wednesday session, the lawmakers gave votes of confidence to Kadhimi's picks for the ministries of interior, defense, finance, and electricity, among others.
However, several ministerial candidates failed to get the lawmakers' approval, meaning Kadhimi will begin his term without a full government.
The parliamentarians rejected the incoming premier's picks for justice, agriculture and trade ministries.
They also postponed voting on the oil and foreign ministries as political parties failed to agree on candidates.
On April 9, Iraqi President Barham Saleh officially tasked Kadhimi with forming a government after the 53-year-old director of the country’s National Intelligence Service received the endorsement of the majority of the top political figures.