The DUP and a lawyer for the family of a murdered RUC officer have accused the Irish government of interfering in the inquiry into his murder.
Chief Superintendent Harry Breen was shot dead along with his colleague Superintendent Robert Buchanan in an IRA ambush in 1989.
The Smithwick Tribunal, set up in 2005, to investigate the deaths has been asked by the Dail to report by June.
The Breen family's solicitor said imposing a time limit was not right.
John McBurney said any attempt "to curtail, confine, restrict and influence the workings of this tribunal, cannot be right."
"The Mahon Tribunal into planning matters where no one was brutally murdered, had to my knowledge, no time limit and had been dealing with planning matters in the Republic, for longer."
The DUP's Jeffrey Donaldson said: "The haste with which the Irish government is trying to wrap up the inquiry into possible Garda collusion in the deaths of Chief Superintendent Harry Breen and Superintendent Robert Buchanan has caused alarm.
"The Smithwick Tribunal was established to get answers about these important questions: it should be allowed to run its full course and should not be interfered with.
"Had the United Kingdom government intervened to order the Saville Inquiry to wrap up early or set deadlines for completion, the Irish government would have raised its concerns."
Irish Justice Minister Alan Shatter denied that the government was interfering in the tribunal's work.
"There's a motion that the cabinet has agreed be brought before the Dail (Irish parliament)," he said.
"It's a motion asking that a report be made by the tribunal to the Dail as to where it now stands with the work done.
"The motion secondly envisages the Dail asking the tribunal to complete its work by 30 November."
Mr Shatter said the November deadline was not set in stone.
"We've been informed by the tribunal chairman that he believes the tribunal will be in a position to do that, but should it emerge that there's a difficulty in that regard, of course, we'll revisit the matter," he said.
"I think it is very important to the families of the two deceased members of the RUC, to everyone who is aware of the tragic background to what occurred, that clarity be brought to where matters now stand."
The Smithwick Tribunal has held some plenary hearings and will make a public statement when it sits again on 7 June.
Oral hearings are due to begin a few days later.
Mr McBurney defended the amount of time the tribunal had been sitting.
"It has been in a private investigative phase for five years because it deals with several jurisdictions," he said.
"It cannot compel witnesses, it has to deal with army personnel who are in England, retired police personal who are in NI.
"The tribunal can only compel witnesses in its own jurisdiction of the Republic, and therefore it has been incredibly complex to obtain documentation from the NIO, RUC, MOD, Garda Siochana.
"It covers the entire breadth and spectrum of the issues that have been under consideration in the various inquiries.
"When you reflect on all of that, is it any wonder that it has taken five years to assemble all of the information and documentation, and it is not all together yet."