The National Crime Agency's Operation Stovewood, which is the UK's biggest investigation into child sexual exploitation, is looking at exploitation and abuse in Rotherham between 1997 and 2013.
But in a parliamentary debate the Yorkshire town's MP Sarah Champion said the council is receiving only £500,000 per annum in extra government funding to help ease the burden.
Children's minister Nadhim Zahawi told yesterday's House of Commons adjournment debate, that the request for extra funds was being considered as part of the government's next spending review, and listed various funding boosts which had already been allocated.
In an impassioned reply, Champion told MPs: "He mentions the half a million a year for four years.
"That will fund 10 looked-after children placements.
"Please, will he just tell me is he going to give us additional funding because we are on our knees in Rotherham and we are begging you for support."
During her earlier speech, she said: "Minister, with the exception of £3.4m of one-off support from the Ministry of Housing, Communities and Local Government in 2015/16 and the half a million pounds of annual funding provided for Stovewood, the council has had to fund these increased costs by making savings for other services and prioritising resources for children's services."
Champion told MPs that the government has failed to support the council's "unique" circumstances and is also concerned that Rotherham will not benefit from the Department for Education's announcement last year of £85m in extra money to assist councils with rising numbers of children in care.
The MP said the council increased the children's services budget by £20m in 2016/17, but demand continues to increase further.
Rotherham Borough Council forecasts an overall £16m overspend for children and young people's services for the current financial year.
This money is likely to go to children's services rated as "requiring improvement" rather than departments that have been awarded a "good" rating, such as in Rotherham, said Champion.
The MP was later reported as saying she was "disappointed" not to have received assurances of extra money.