"Is it not now time, rather than wake up every week to see a new institution involved in this mire, that we have an overreaching, robust public inquiry into the whole failings of child protection?" lawmaker and ex-children's minister Tim Loughton asked the House of Commons.
Yvette Cooper, the main opposition Labour Party's spokeswoman on home affairs, also called for a single national inquiry.
"We remain concerned that these multiple inquiries have no way to draw together the common themes, the problems, the lessons that need to be learned," she said.
Last month a TV documentary detailed alleged abuse by Savile, who died last year. Police have called the claims a "watershed moment" that has given some victims the confidence to contact authorities for the first time.
Detectives are examining claims from about 300 possible victims that they were abused by Savile and a group of people associated with him.
May told lawmakers that the priority was to allow police to conclude their inquiries, but said the government would not rule out a large-scale study of issues raised.
"If ... it appears that it is necessary to move forward to a wider investigation then we will look at that," she said.