Conservative party chairman David Davis opened a special debate on the affair in the House of Commons on Tuesday.
Computer Weekly has campaigned to overturn the finding of gross negligence against RAF flight lieutenants Jonathan Tapper and Richard Cook over the crash, in which 25 high-ranking police and intelligence personnel were killed. It has highlighted the fact that possible problems with the helicopter's engine control software cannot be ruled out as a cause.
The Ministry of Defence has persistently refused to change the verdict despite critical reports from a special House of Lords investigative committee and the Commons Public Accounts Committee.
Efforts to persuade the Government to reverse the verdict are being supported by the Liberal Democrats, the Scottish National Party and some Labour backbenchers.
Before the debate Davis said, "It is, I think, unprecedented that we have an all-party motion on an opposition day. It is an apolitical issue. Six weeks ago, the House of Lords report came out and it was devastating for the MoD's case.
"We want to bring the MoD's thinking process into the public domain. What it says, time and time again, is that no new evidence has been brought up. The answer to that is that there was never any evidence in the first place.
"Every breakthrough is preceded by the feeling that you are banging your head against a brick wall."
Labour backbench MP Frank Field said, "If the Government does not listen to every political party, then something is deeply wrong. When members of all sides of the House come together on a motion it has to be addressed. We want to see justice and we want to see the pilots exonerated."
The motion reads, "That this House notes the House of Lords Select Committee Report on Chinook ZD576, which concludes that 'the air marshals were not justified in finding that negligence on the part of the pilots of ZD576 caused the crash' in the Mull of Kintyre on 2 June 1994; and calls on the Government to exonerate the deceased pilots, flight lieutenants Jonathan Tapper and Richard Cook."
The wording closely follows an early day motion tabled by Angus Robertson, the Scottish National Party's Westminster defence spokesman, in February 2002, which has already secured the support of 79 MPs.
Robertson said, "I am very pleased to be co-operating with members from other political parties in the campaign to exonerate the Chinook pilots. This is a strong campaign, and I am convinced that a cross-party effort can be successful in persuading the Government to change its mind.
"Already, 79 MPs have backed the early day motion that I tabled, and I believe that most MPs and members of the public are persuaded of our case. This debate is part of the process of winning justice for the pilots' families, and removing the stain from the memories of their loved ones."