Identifying who made offensive changes to a Wikipedia page about the Hillsborough disaster "may prove challenging", ministers have said.
The government said a full inquiry led by Cabinet Office Permanent Secretary Richard Heaton was under way.
It came after the Liverpool Echo said Whitehall computers on a secure government network were used.
The Cabinet Office said the "sickening" changes were "in complete contravention of the Civil Service Code".
'All relevant material'
A Cabinet Office statement said "important stakeholders" including the Hillsborough Family Support Group, the Hillsborough Justice Campaign and the All Party Parliamentary Group on the Hillsborough Disaster would be kept updated of developments.
A spokesman said Andy Burnham MP, who "has a deserved status as an expert on the disaster", would be given the chance to "view all relevant material from the very outset so that he can assure himself all steps have been taken".
The statement said: "The amendments made to Wikipedia are sickening. The behaviour is in complete contravention of the Civil Service Code. It is entirely unacceptable.
"At this time, we have no reason to suspect that the Hillsborough edits involve any particular department, nor more than one or two individuals in 2009 and 2012.
"As the first incident happened five years ago and there are hundreds of thousands of people on the government's network, it may prove challenging to identify who was involved, but we are exhausting every option."
Mr Burnham said it was "sickening and appalling to think that people in government are aiming this kind of abuse at the Liverpool supporters - particularly the victims and survivors of that tragedy".
He said that "a full and proper inquiry [to] find the name of the individual or individuals responsible" needed to happen, adding that they must then be "held accountable - nothing else will do".
Mr Burnham, during his time as Culture, Media and Sport Secretary, was instrumental in a campaign to have classified documents about the disaster released, which led to the formation of the Hillsborough Independent Panel.
Oliver Duggan, the Liverpool Echo reporter who broke the story, said the paper used a list of 34 internet protocol (IP) addresses for Whitehall computers.
These were released in 2008 by Angela Eagle MP following a parliamentary question to "match up" the addresses with those used to edit the Wikipedia page about the disaster.
The newspaper said the alterations to the page included the Liverpool anthem You'll Never Walk Alone being altered to You'll Never Walk Again and the phrase "Blame Liverpool Fans" being added to a paragraph.
Steve Rotheram, the MP for Liverpool Walton, echoed Mr Burnham's remarks and said he and a group of Merseyside MPs would be writing to the government to ask that any inquiry "be swift".
Sheila Coleman, spokeswoman for the Hillsborough Justice Campaign, said the group would be talking to its legal team about "how to proceed".
Ms Eagle, the MP for Wallasey, said the claims were "pretty shocking" and were "another problem for [the families] having to deal with the grief".
Entries in Wikipedia, an online encyclopaedia, can be edited by anyone with access to the internet.
Jon Davies, chief executive of Wikimedia UK, said it was "appalled by such vandalism".
Ninety-six Liverpool football fans died after a crush at an FA Cup semi-final at the Sheffield ground on 15 April 1989.
New inquests, which are ongoing, were ordered after fresh evidence revealed by the Hillsborough Independent Panel led to the original inquest verdicts being quashed.