Relatives of the murdered solicitor Pat Finucane have not received any assurance from the British Government that a public inquiry into his death will be called.
His family met the new Northern Ireland secretary, Brandon Lewis, at Stormont on Friday.
Tanaiste Simon Coveney is also due to meet Mr Lewis soon.
Mr Finucane was shot dead by loyalist paramilitaries in 1989. There have been long-standing allegations that members of the UK security forces colluded in his murder.
His family has been urging the government to hold a public inquiry into the case.
Assessment 'within weeks'
In January, his widow, Geraldine Finucane, was granted leave by the High Court to seek a judicial review as part of her ongoing campaign to secure a public inquiry into her husband's death.
After meeting Mr Lewis, Mrs Finucane said she had not heard anything to indicate an inquiry will happen yet.
She added that the secretary of state told her he would make an assessment "within weeks, not months".
Her son, the Sinn Féin MP John Finucane, said this was the first time they had secured a meeting with the British government, despite requests to his predecessors, Julian Smith and Karen Bradley.
Mr Lewis has also met Tánaiste (Irish deputy prime minister) Simon Coveney at Stormont.
It was their first meeting since Mr Lewis replaced Julian Smith.
Mr Coveney says he has impressed upon the new Secretary of State the need to implement legacy plans "in full".
The pair held their first official meeting at Stormont on Friday afternoon.
Mr Coveney said Mr Lewis faces "a number of challenges" in his new role.
In the latest Stormont deal, the government pledged to introduce legislation - within 100 days - to implement a legacy deal struck five years ago.
It includes an Historical Investigations Unit (HIU) to look into Troubles killings - a proposal that jars with calls from some Conservatives - and a commitment from Number 10 to end all "vexatious prosecutions" against former Northern Ireland veterans.
There was speculation Julian Smith had "blindsided" Boris Johnson over that element of the New Decade New Approach deal - a claim Mr Smith has denied since he was sacked from the NI portfolio.
Mr Coveney paid tribute to Mr Smith, saying he was a "tough act to follow" - but that he would work with Mr Lewis to uphold all aspects of the deal.
He also said he had discussed Brexit with the new secretary of state.
The meeting follows the Irish general election, which saw Mr Coveney's Fine Gael party come in third place.
That government, under Taoiseach (Irish prime minister) Leo Varadkar, will remain in place until a new government can be formed.
Mr Lewis made his first official visit to Northern Ireland last week, when he said he was "fully aware" of his responsibilities and that he was focused on making "a brilliant success of the New Decade, New Approach deal".