MLAs from the two parties clashed during a meeting of the Preparation for Government Committee which was discussing decommissioning and criminality and paramilitary activity.
The argument was sparked when Sinn Fein rejected a series of motions tabled by the DUP supporting the police and
renouncing crime.
Afterwards, DUP MLA Ian Paisley Jnr said: "These are the people that want to be in government tomorrow but won't agree to the upholding of the law of the land.
"This is further proof that republicans remain totally unfit for office and have a lot to do to make themselves fit for ministerial positions."
Sinn Fein responded by saying it was the DUP that had to come up to the mark – on power-sharing.
"They are the only remaining blockage to restoring the political institutions," said Alex Maskey.
"Other outstanding matters such as policing can only be
resolved in the context of functioning political institutions."
Sinn Fein:
* were unwilling to support the PSNI
* rejected the idea of naming and shaming individuals and organisations involved in drug dealing, and
* refused to support the call for an inventory of the material decommissioned by the IRA to be made public.
In a joint statement after the PFG meeting, MP Sammy
Wilson and MLAs Mr Paisley and Peter Weir said republicans were the real blockage to the return of devolution.
"Support for the police and the rule of law in Northern Ireland are clearly fundamental requirements for any democratic society," they said.
"While Sinn Fein were prepared to spout the rhetoric of
opposition to criminality and the blight it is on society (during the PFG meeting], they were not prepared to take the steps necessary to eradicate it.
"Their so-called opposition to crime rings hollow when it is not combined with a call for people to report crime and support the police.
"Once again this demonstrates that Sinn Fein have still some distance to travel before they can be considered to be fit for government.
"Opposition to support for the rule of law is incompatible with the holding of ministerial office, and it is clear that Sinn Fein will have to address some serious issues before they can hope to take up a place in any future Executive."
SDLP Policing spokesman Alex Attwood admitted "major differences" around issues of law, order and justice remained but insisted there had been some "surprising agreement".
All parties on the committee welcomed the agreement that there would be a single justice ministry and agreed that the shape and model of the new ministry needed to be worked through by the parties "collectively", he said.
"If this good work can be built on by the parties talking and negotiating together, more progress might be made."