Details of emailed correspondence between a top civil servant and another senior Downing Street official were highlighted in court as lawyers pressed for complete disclosure of notes or recordings from a series of ministerial meetings.
The family want the material as part of their legal challenge to the British Government's refusal to order a full, independent probe into the 1989 assassination.
On Thursday, the High Court heard how one of David Cameron's closest advisors described the murder of Belfast solicitor Pat Finucane as far worse than anything alleged in Iraq or Afghanistan.
Sir Jeremy Heywood, now the Cabinet Secretary, also questioned whether the Prime Minister believed it was right to "renege" on a previous administration's commitment to hold a public inquiry into a killing he referred to as "a dark moment in the country's history", a judge was told.
A review carried out by lawyer Sir Desmond de Silva QC and published in December confirmed agents of the state were involved in the murder and that it should have been prevented.
However, it concluded there had been no overarching state conspiracy in the shooting, carried out by the loyalist Ulster Freedom Fighters at the solicitor's north Belfast home.
Although Mr Cameron expressed shock at the level of collusion uncovered by Sir Desmond, Mr Finuncane's widow, Geraldine claimed it was a sham and a whitewash.
Opening the family's application for discovery of the documents, Barry Macdonald QC said the case was about past and present abuse of state power.
Mrs Finucane knows the name of the person who pulled the trigger. The question is who was pulling the strings?
Barry MacDonald QC
The first instance in 1989 involved the murder of a solicitor perceived to be "a thorn in the side" of the government, police and security services, he claimed.
Mr Macdonald continued: "Secondly, it's about abuse of power in 2011 by the current government when it decided to renege on a solemn commitment to conduct a public inquiry into those events in 1989."
The full scale of what went on has yet to be revealed, according to the barrister.
In a 500-page report by Sir Desmond de Silva, consideration of the government's role takes up five pages.
Stressing the gravity of the case, Mr Macdonald detailed an email Sir Jeremy sent to Simon King, a private secretary to the Prime Minister, ahead of a ministerial meeting in July 2011.
In correspondence already disclosed to the parties, he asked: "Does the PM seriously think that it's right to renege on a previous government's clear commitment to hold a full judicial inquiry?
"This was a dark moment in the country's history - far worse than anything that was alleged in Iraq/Afghanistan.
"I cannot really think of any argument to defend not having a public inquiry. What am I missing?"
A reply email stated that the Prime Minister "shares the view this is an awful case, and as bad as it gets, and far worse than any post 9/11 allegation", the court heard.
According to Mr Macdonald, the exchange provided a flavour of the seriousness of the alleged abuse of power in not holding a public inquiry.
He said it involved weighing any commitment by a previous government against current public interest.
Mr McLaughlin also pointed out that retired Canadian Judge Peter Cory had already examined the case and concluded there should be a public inquiry.
He argued that some of the material being sought would not advance the plaintiff's cause any further.
The hearing continues.