The DUP's Jeffrey Donaldson has accused the British government of creating a "hierarchy of victims" in Northern Ireland over its funding of investigations of unsolved killings during the Troubles.
The SDLP has also criticised the government, calling for the Historical Enquiries Team (HET), which is investigating more than 2,500 "cold cases" since 1969, to receive its full cash allocation of £34 million (€50 million) upfront.
Mr Donaldson, the Lagan Valley MP, accused the government of failing to provide adequate funds for the HET, forcing it to draw on some £4 million from the general policing budget.
"It is totally unacceptable that the government should fail to honour a commitment to properly fund the HET and it is also unreasonable that money allocated had to be taken from the chief constable's budget," he said.
"The government must give the issue priority. With over 3,000 unsolved murders it is totally unacceptable that the funding of these inquiries should have to come from the policing budget.
Comparing the HET allocation of £32 million over six years to the £150 million spent on the Bloody Sunday inquiry, Mr Donaldson added: "You are looking at a hierarchy of victimhood where some victims are given priority over others."
The SDLP's Dolores Kelly, a member of the Assembly and the Policing Board, said the manner of the HET's funding was "alarming".
"The chief constable should not have to choose between combating crime and investigating the past," she said.
"HET should have got the £34 million it needed upfront. The British government promised victims truth and justice and offered the HET as an alternative to public inquiries. It has now crippled the public inquiry system in the name of political expediency, and it cannot be allowed to strangle the HET on the same grounds," she said.
The HET, established in 2005, comprises more than 100 police officers from a range of police forces. Some 693 murder files have been reopened.