Published Saturday, 19 July 2014
The June Monitoring Round has yet to be agreed because of disagreement over welfare reform.
Mr Robinson says it will be impossible to sign off funding for the Historical Institutional Abuse Inquiry (HIA) and other projects because of the hold-up in agreeing the overall funding package.
The inquiry was set up by the Executive and is looking into abuse in local care homes between 1922 and 1995.
The inquiry team is due to report to the Executive by the start of 2016.
The DUP leader said: "The Executive has already approved the payment for Historical Institutional Abuse Inquiry subject to the approval of June Monitoring Round.
"If you don't get the money through the monitoring round then there is no funding to allow Judge Anthony Hart to proceed with the inquiry and that would be an outrage if that were to happen."
He added: "The HIA would have to be suspended if there was no money for it.
"The accounting officer in the department couldn't allow money to be spent if there is no approval for it.
"I think within the next number of days there has to be a very real attempt made by everyone to resolve all of these issues."
I don't see us getting to that tragic set of circumstances and I don't want to raise alarm that it is something that is going to happen.
"We know what the British Government's position is over welfare reform, there will be no more concessions. The only thing that can change is Sinn Féin.
"This is not the DUP saying one thing and Sinn Féin saying another, this is happening, this is reality."
Sinn Féin MLA Alex Maskey, who sits on the OFMDFM scrutiny committee, rubbished Mr Robinson's claim the inquiry was under threat.
He said: "What Peter Robinson is doing is he is picking one project over another project.
"There are a lot of projects which may suffer if the DUP want to impose the type of cuts that they are talking about.
"The DUP could just as easy say they are going to stop something else and they have been doing that in a very sustained drip feed manner."
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