Prime Minister Haider al-Abadi has ordered Iraq's three vice presidential positions to be scrapped and their funding reallocated as part of a reform drive aimed at curbing rampant corruption and government waste in response to weeks of protests.
Masum called on his website for "protecting the constitution... And not bypassing it and not stopping working with it."
He did not reject proposed changes outright, but said they must be carried out in keeping with the constitution.
Abadi, in a statement on his website, said "the reforms voted on by the cabinet and the parliament are constitutional and legal and I will not back down on them."
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Zaid al-Ali, a constitutional expert and author of "The Struggle For Iraq's Future," said removing the position of vice president would require the charter to be amended.
Amid a 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.
Abadi rolled out a reform programme two days later that included eliminating the positions of deputy prime minister, which is apparently within his power, as well as those of the vice presidents.
Parliament signed off on those proposals and on additional reforms, and Abadi has begun issuing orders for changes, including cutting 11 cabinet posts and slashing the number of guards for officials.