The Foreign Office minister, Christopher Pincher, told lawmakers on Tuesday that it would be "some time" before the report was published, adding: "When the prime minister has concluded that the report is publishable he will publish it."
British members of the European Parliament on Wednesday piled more pressure on Johnson to publish the report.
A group of 16 of them from multiple political parties, led by Labour's Julie Ward, signed a letter calling for its "immediate publication."
It said: "We believe for our constituents and the country that this is a matter of grave urgency; the country must go into the upcoming General Election knowing that it is free and fair from outside meddling.
"If the publication cannot be made available due to the sensitive nature of the matter, the government should respond accordingly outlining what is preventing it from being made public.
"As this cross-party letter shows, this is not about political ideology it is about the foundation and fundamentals of our democracy. We must have transparency and we must have scrutiny across all levels of government."