Mr Mahmood claimed the youngster had been removed from school by her mother 10 weeks ago.
He said there should be an inquiry into what action was taken by officials and pledged to write to the chief executive of Birmingham City Council.
He accused the council of "battening down its hatches", by instructing its officers not to comment.
"They're accountable to the people of my constituency, of the family where the young child has lost its life. And they're accountable to all of us, " he said.
"They're not there to just do as they wish. They're there to serve the people of Birmingham. And this attitude of battening down the hatches isn't constructive."
He added the reason he was asking for an inquiry was to see if the council could say what had gone wrong and what issues needed to be looked at in the future.
Home Secretary Jacqui Smith, in Birmingham on Thursday, said she was shocked by the case and supported Mr Mahmood's inquiry call.
"What I think is important is we, as the local MP has called for, look very carefully at the background of the case before coming to any immediate conclusions.
"But it's a tragedy and I feel desperately sorry for those who knew the young girl," she said.
Parents dropping children off at Grove School, Handsworth, where Khyra was a pupil, spoke of their shock at her death.
Renata Palczewska, 26, said: "The teacher, when she told me, was almost in tears. She was very upset. She knew the girl.
"The school gave us a letter but they couldn't give us much information.
"I can't believe this could happen. You would expect someone to notice."
Flowers outside a house in Leyton Road, Handsworth
West Midlands Police said in a statement: "We can confirm that a seven-year-old girl was taken to hospital on Saturday 17 May, where she was pronounced dead."
The statement added: "Her cause of death has not been confirmed at this stage.
"Police are conducting inquiries and a man aged 29 and a woman aged 33 have been charged with neglect and appeared before Birmingham magistrates on 19 May.
"They have been remanded to appear again on 28 May.
"As proceedings are active, we cannot comment further at this time."
A Birmingham City Council spokesman said: "We are deeply saddened by the death of this child and our sympathies go to the child's family and friends at this difficult time.
"This death is now the subject of a police inquiry and Birmingham City Council are fully supporting the investigation.
"We are therefore unable to make any further comment."
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