Analysts expected Ahmadinejad to face stiff opposition over some of his nominees.
Some members of parliament have said they are likely to reject several ministerial nominees because of their lack of experience.
Parliament will vote on the individual nominees on Wednesday.
The vote of confidence comes as Iran is gripped in political turmoil after Ahmadinejad's re-election triggered massive street protests which left about 30 people dead.
Al Jazeera's Alireza Ronaghi, reporting from Tehran, said Ahmadinejad was facing a difficult task to convince parliament that his nominees were the most suitable.
"It's not going to be easy for Ahmadinejad. He has to convince some parliamentarians who are not at all convinced about the capabilities of his choices.
On July 18, 1994, a bombing at the Argentinian Jewish Mutual Association in Buenos Aires killed 87 people and injured more than 200.
Prosecutors on the case accused Iran-backed Hezbollah of carrying out the bombing and accused senior Iranian officials of planning the attack.
Iranian officials have strongly denied any involvement.
Interpol issued an arrest notice for four senior Iranian officials, including Ahmad Vahidi, Ahmadinejad's defence minister-designate.
"The problem with Ahmadinejad's choices is that in some cases he has kept ministers who have been criticised for mismanagement in the past.
"And in some cases, he has replaced ministers who have been praised for what they have done, even by the president himself.
"The parliamentarians have shown that they don't like Ahmadinejad's attitude of just sacking whoever says one word in opposition with him so they're going to question him very hard," Ronaghi said.
Ali Larijani, the parliament speaker, opened the debate session on Sunday.
"We hope in the following friendly sessions the members will hold the debates with dignity and patience and pursue the matter with Islamic ethics.
"The majlis [parliament] will provide ample time for both sides to present their cases," he said.
Ahmadinejad's proposed cabinet line-up includes three women, for the posts of education, health and social welfare. They would be the first female ministers in the country.
His choice of Ahmad Vahidi as next defence minister has been controversial after an outcry in Argentina, where he is wanted for the 1994 bombing in Buenos Aires of a Jewish community centre that killed 85 people.
Ahmadinejad has retained five ministers from his existing cabinet in the same capacity in the new line-up, including Manouchehr Mottaki, the foreign minister.
Mostafa Mohammad Najjar, the current defence minister, has been nominated as the next interior minister while Masoud Mirkazemi, the commerce minister, has been suggested as head of the oil ministry.