The report was produced by Parliament's Intelligence and Security Committee (ISC) before the general election but has yet to be published.
It cannot be released until the ISC is reconvened and the SNP's Westminster leader, Ian Blackford, a member of the committee until April 2019, urged the Prime Minister to act.
In a letter to Mr Johnson, he claimed the Government had "repeatedly and intentionally failed to take steps to establish the committee and has sought to escape scrutiny on vital issues".
He told the Prime Minister: "The decision by your Government to kick the publication of a key report into Russian interference into the long grass is disgraceful, and it is clear that it has been delayed without justification by Downing Street."
The Prime Minister has cleared the ISC report, meaning it can be published once the committee is re-formed.
The ISC oversees the work of the intelligence agencies - MI5, MI6 and GCHQ - and in the course of its work has access to highly sensitive material.
Mr Blackford said: "Boris Johnson's repeated refusal to publish a key report into Russian interference in UK democracy, and his intentional delay in convening the Intelligence and Security Committee, is nothing short of an abdication of duty as Prime Minister and a clear attempt at ducking scrutiny."
The push for the release of the report comes a day after Mr Johnson met Russian President Vladimir Putin in the margins of a summit in Berlin.
Downing Street said the Prime Minister made clear there had been no change in the UK's position in relation to Russia following the Salisbury nerve agent attack which was a "brazen attempt to murder innocent people on UK soil" and "must not be repeated".
"The Prime Minister said there will be no normalisation of our bilateral relationship until Russia ends the destabilising activity that threatens the UK and our allies and undermines the safety of our citizens and our collective security," a Number 10 spokesman said.