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".

Inspectors criticised teaching and leadership at the Phoenix Academy and Lakeside Academy following visits in February, rating both schools inadequate in all areas.
Wrockwardine Wood and Sutherland academies, also run by the Telford Co-operative Multi-Academy Trust, were put in special measures earlier this week.
The trust has not commented.
Ofsted criticised the trust's lack of support to the schools and said each was now considering an alternative sponsor.
Inspectors said pupils' achievement at the Phoenix Academy had dropped since it became an academy in 2013 and their latest report rated it inadequate in all areas.
A report in 2013, before it converted, rated the secondary school as "requiring improvement", while Lakeside was rated "good" in 2012 under its former name the Lord Silkin School.
In the latest report, inspectors said the curriculum at Phoenix Academy was "inadequate", while "weak teaching" meant pupils were not sufficiently challenged and were often "disengaged and disruptive".
There was particular criticism of standards in English and maths which the watchdog said were limiting pupils' achievements in other areas.
Ofsted's report said governors, managers and teachers had developed a "culture of low expectations", while leaders had failed to act decisively to halt the decline in pupils' achievement.
There was, however, some praise for the acting head teacher. Inspectors said he had introduced a number of improvement measures and some were "beginning to have an impact".
A report on Lakeside School highlighted similar concerns, criticising teachers for not sufficiently challenging pupils and for having "over generous" predictions of their achievement.
Inspectors said many pupils, whether high achievers or those with special educational needs, were "not making the progress they should" and achievements at GCSE were well below the national average.
Governors were also criticised for not holding leaders to account, while the report said management had failed to effectively monitor either pupils or teachers.
Inspectors, did however highlight new initiatives to improve literacy which they said were "beginning to have a positive impact".

The man, in his 20s, was the only person in the BMW convertible when the accident happened on the A323 Aldershot Road in Guildford.
He was travelling east when his car left the road near the junction with Holly Lane at 23:00 BST on Monday.
Police closed the road between Frog Grove Lane and Holly Lane while investigators were at the scene. Officers have appealed for witnesses.
Police investigations into claims of historical child abuse should "take precedence" over a UK government-ordered inquiry, a Welsh MP says.
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All four schools run by a Telford academy trust have been put in special measures within a week.
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A driver died when his sports car hit a tree on a main road in Surrey.