An independent assessor is to be appointed to advance a compensation campaign by victims of Libyan-sponsored IRA violence.
The Foreign Office said the assessor would be from a legal background.
The work would include assessing how many people could potentially qualify and what levels of redress should be requested.
Libyan leader Muammar Gaddafi supplied weapons, including Semtex explosives, to the IRA during the Troubles.
Libya compensated US victims of terrorism, but UK victims were left out of the deal.
Representatives from both the DUP and Ulster Unionists were among parliamentarians who met with Foreign Secretary Jeremy Hunt over the issue on Monday night.
“Our objective was to repeat the case for Libya to put in place a compensation scheme for the victims of the PIRA campaign in the 70s and 80s,” the DUP’s Emma Little-Pengelly said.
“The UK has a strong case, but we must keep the campaign alive.”
The UUP’s Lord Empey said he was “slightly encouraged by his [Mr Hunt’s] decision to appoint an independent assessor”. Gaddafi supplied weapons to the IRA during the Troubles.
He added: “While no firm undertakings were given by the foreign secretary, the fact is that this is the first time that the government has done anything other than bat the problem away, which is what has been happening from the time when Tony Blair was prime minister.
Suzanne Dodd, whose police officer father Stephen Dodd was killed in the Harrods store bombing in 1983, said the measure did not go far enough.
This week marked the 35th anniversary of the IRA bomb at the London store where six people were killed and 90 injured.
“Yes, it is a small step, but what we have to deal with at the moment is I am one of the youngest victims of the Harrods bombing and I am 42 years old,” Ms Dodd said.
“My father, for instance, they have all gone.
“It has a big knock-on effect, that everyone is getting older and the British government are just waiting for us to die.”