Ms Mowlam was responding to questions after yesterday's disclosure in The Independent that Dublin strongly suspects elements of British intelligence were deeply involved in many loyalist murders of republican suspects.
The Irish government made no response to the report, which was based on a confidential, 11-page document conveyed by Dublin to Ms Mowlam last month. It has already called for a full-scale public inquiry into the killing.
The document said there were patterns "which tend to confirm widespread suspicions that elements in the security forces were used, at the expense of the rule of law, to prosecute a campaign against those deemed enemies of the state and to conceal what that entailed and who was culpable".
Responding to the report Ms Mowlam said: "I take the situation very, very seriously. I am determined that no option will be excluded. Be assured, I am not going to leave the issue alone."
Referring to the recent reopening of the Finucane investigation under the Deputy Metropolitan Police Commissioner, she added: "If there is a chance of a prosecution, I am going to see it, and see that the findings of the Stevens investigation go to the DPP. I am not going to let this drop. If I can get a prosecution, I am not going to lose it just because of pressure."
Meanwhile, the UN special rapporteur on judicial independence who reported last year on the Finucane murder, Param Cumaraswamy, said Dublin's stance supported the calls he had made for an independent judicial inquiry.
He added: "My concern was in connection with whether the security forces and/or the RUC knew this particular murder was going to take effect, and if so, I asked why wasn't Pat Finucane protected.
"I think the situation has come to a level now that it is going to be a little difficult for the UK government to refuse a judicial inquiry. I am concerned whether security forces were involved and if so, then I think that the UK government had an obligation to protect the life of Pat Finucane."
The Ulster Unionist security spokesman, Ken Maginnis, however, told the BBC that "there was no need for collusion" in the Finucane case, saying the lawyer had been a member of a well-known republican family.
Ms Mowlam also yesterday welcomed a meeting held last night to discuss the Drumcree Orange march in July, which is once again threatening to produce disorder.
The meeting was convened by the local MP, David Trimble, who is also Northern Ireland's first minister designate. It was boycotted by senior members of the Orange Order, who disapprove of the idea of face-to-face meetings with Catholic residents of the Garvaghy Road district of Portadown. A number of local councillors and other Protestant representatives were set to attend.
Ms Mowlam said: "Drumcree is a situation which will make such a difference if we can find an accommodation. It's talking between the two sides which will make progress and I wish them well, all those who have decided to start talking. That is a big, big, plus."
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