In a statement on his Facebook page, Mr Robinson called on the parties to take care the positions they are adopting do not close off sensible options.
He advised the politicians to "step back, take a breath".
He said they should ensure there is space for an agreement "in the calmer times that follow the hustings".
Mr Robinson wrote that he had been determined not to provide a running commentary on political events since he stepped down.
However, he said his concern for the existence of the Stormont institutions has overridden his desire for a quiet retirement.
The former DUP leader acknowledged that mistakes were made over the Renewable Heat Incentive (RHI) scheme.
But he argued that the executive's proper role should have been to put in place cost control measures and initiate a thorough inquiry.
Mr Robinson said the argument that it was "time for the people to have their say" was bogus.
He added that he could not help feeling that if Martin McGuinness had been in good health, the breakdown would have been avoided.
Instead, he argued, "more belligerent elements" in Sinn Féin had "seized their opportunity".
The former first minister said he believes a major negotiation of the kind Sinn Féin is seeking cannot be completed in the time legally available before a fresh election should be triggered.
"Almost inevitably, the assembly will be suspended and Northern Ireland will be back to direct rule," he said.
Mr Robinson said the election had "constitutional importance" and he called for a high unionist turnout.
Former first minister Peter Robinson has said that "while the election is unstoppable the headlong rush into destruction is not".