The ICC launched a probe after the "Cricket's Match Fixers" programme showed a groundsman agreeing to tailor pitches for Test matches involving leading teams.
"I ask Al Jazeera to release to us all the material they have relating to corruption in cricket," Richardson said in a statement on Friday.
"We will conduct a full, thorough and fair investigation and ensure no stone is left unturned as we examine all allegations of corruption made in the programme. To do so, we need to see all the evidence they state they possess."
The programme alleged that the stadium manager at Galle Stadium in Sri Lanka may have doctored the pitch under the influence of fixers. It also alleged that minor Twenty20 events had also been targeted.
Furthermore, there have been spot-fixing incidents in a Chennai match between England and India in December 2016, it alleged, and the Australia-India Test in Ranchi in March 2017.
"We understand and fully respect the need to protect journalistic sources and our ACU (Anti-Corruption Unit) team have worked with other media companies on that basis," Richardson added.
"However, to prove or disprove these allegations, we need to see the evidence referred to in the programme," he added.
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