Cardiff North MP Jonathan Evans said it was "a tragedy" there was no agreement on who should chair the inquiry, set up after claims of paedophiles operating in Westminster in the 1980s.
The Conservative MP said cases should be investigated by the police first.
Child abuse survivors have urged the government to scrap the inquiry.
Instead, they want it replaced with a more powerful body.
It comes after Home Secretary Theresa May told inquiry members their panel might be disbanded.
The Met Police said earlier this month that detectives were investigating three alleged murders as part of their investigation into historical child abuse.
Mr Evans, who is chairman of the Welsh Tory party and a former deputy chairman of the Welsh NSPCC council, said: "Now I hear that a number of the groups who are representing victims have suggested the whole of the process should be stopped and a different sort of inquiry created.
"I don't know exactly what the terms of that inquiry should be and I'm not really sure what they mean by setting up a stronger inquiry because I think the inquiry that was being set up was a pretty strong one."
He said ongoing police inquiries introduced a "new dimension", and that they appeared to be proceeding on the basis of new evidence "in which the police have already made it clear to the media that there are real issues that are being investigated".
"It seems to me that those police inquiries have got to now take precedence. We ought not to have a situation in which we set up an inquiry and then we can only do half the job because police inquiries are ongoing."
Mr Evans, who was a Wales Office minister in the 1990s when the UK government set up the Waterhouse inquiry into abuse allegations at children's homes in north Wales, added: "It seems to me that the police inquiries are now at the forefront."
He said Mrs May should not be blamed for delays to the inquiry, which has been held up by the resignation of her first two choices of chairperson.
Victims must have confidence in the process, Mr Evans said, "and so the reason we are in the situation we are in is that we are struggling to find a chairman that the victims' groups will have confidence in".
Police investigations into claims of historical child abuse should "take precedence" over a UK government-ordered inquiry, a Welsh MP says.