The FA has been too slow in reacting to allegations of sexual abuse in football and must launch a "much wider" inquiry, Conservative MP Damian Collins says.
The culture, media and sport committee chairman told the BBC the FA review into claims ex-players were abused as children needed to establish if there was a cultural problem in the sport.
The FA's internal review will look at what officials and clubs knew and when.
Governing body Fifa said it was monitoring the situation closely.
Four police forces say they are now investigating historical allegations of child sex abuse.
On Sunday, the FA instructed independent leading counsel Kate Gallafent QC to oversee its internal review, saying it would look into "what information the FA was aware of at the relevant times, what clubs were aware of, and what action was or should have been taken".
The FA said it was working closely with police, adding it "must ensure we do not do anything to interfere with or jeopardise the criminal process".
However, Mr Collins told BBC Radio 4's Today programme that while the FA announcement was a "step in the right direction", it could be doing more.
He said the governing body could have been "quicker out of the blocks", adding: "This internal review needs to go much wider.
"They need to make it clear that this is a full investigation, the person leading it can take it in whatever direction they want, that anyone in football who is called as a witness is compelled to give evidence.
"I think, crucially, it shouldn't just investigate individual allegations made in the past, but ask the question, 'Should people in football have known more?'"
He said the investigation should also assess whether there were problems with "the whole culture of football", and it was vital its findings were published in full.
Former sports minister Richard Caborn told the programme "real concerns" about the protection of young people in football - and other sports - existed when he was in government in 2001.
"I met officials from the NSPCC at that time," he said, adding that he had pressed for independent structures and a whistleblower hotline to be set up, but nothing had happened.
The Hampshire, Cheshire, Northumbria and Metropolitan police forces have all opened investigations following recent allegations.
They come after former players including David White, Andy Woodward, Steve Walters and Paul Stewart have spoken out about abuse.
Ex-Crewe player Woodward, 43, went public on 16 November about his abuse by former Crewe coach and youth football scout Barry Bennell, who was later convicted of sex offences against children.
Former youth team players Chris Unsworth and Jason Dunford also told BBC's Victoria Derbyshire programme they had been abused by Bennell.
Professional Footballers' Association (PFA) chief executive Gordon Taylor says more than 20 former footballers have come forward regarding allegations of sexual abuse.
Taylor said at least "six or seven clubs" including Crewe, Manchester City, Blackpool, Leeds, Stoke and Newcastle were connected with "particular individuals".
Blackpool released a statement saying the club was "yet to receive any information from the PFA or relevant authorities in relation to the ongoing investigations of historical abuse".
Leeds also said it had not been made aware of any allegations, but would "take any such complaints seriously and will cooperate fully with the PFA and the FA with any investigations".
Fifa said in a statement: "We are aware of the allegations. Fifa considers the protection of children and young people as fundamental in football and we will monitor the situation closely."
Have you been affected by the issues raised in this story? You can email email@example.com with your experience.
Please include a contact number if you are willing to speak to a BBC journalist. You can also contact us in the following ways: