Sinn Féin has insisted that unionists must accept as legitimate the party's democratic credentials.
Responding to yesterday's Irish Times article by Mr Peter Robinson, Mr Mitchel McLaughlin, the party chairman, said: "It is time for the DUP to respect Sinn Féin's mandate." The DUP deputy leader had written that the holding of a mandate did not mean a party was necessarily democratic. He said republicans had to remove all traces of paramilitary and criminal activity before political progress which enjoyed the confidence of unionists could be made.
Mr McLaughlin said the DUP had to "concentrate on the job of agreeing a package which will quickly see the political institutions re-established and all other outstanding issues dealt with".
Overlapping some of the comments made by Mr Robinson, Mr McLaughlin added: "The issues which need to be addressed as part of a comprehensive package have been identified. Nationalists and republicans acknowledge that there are issues of concern for unionists."
Turning to the crunch issue for Sinn Féin, he said: "If the DUP accepts that the range of issues which are of concern to nationalists and republicans must be dealt with, including the core issue of transfer of policing and justice powers away from London, then our collective responsibility is to move quickly to resolve these issues."
Mr McLaughlin said the DUP must now act on the reality that Sinn Féin represents the majority of nationalist opinion and dedicate itself to "agreeing a package which will quickly see the political institutions re-established and all of the other outstanding issues resolved without further delay".
The SDLP's Mr Alex Attwood said he recognised Mr Robinson's "more helpful tone" and some "helpful content" in his Irish Times article.
Mr Attwood, Assembly member for West Belfast, said the DUP deputy leader's "apparent new realism about the nature of our politics is to be welcomed".
However he went on to accuse both unionists and Sinn Féin of being "found wanting in the white heat of negotiations". He said there was enough in the recent Irish Times articles by Mr Gerry Adams and Mr Robinson "to conclude that they will be found wanting again".
Sources on the nationalist side, while publicly criticising aspects of the current unionist position, nonetheless accept there are positive elements to the current political tick-tacking in advance of next month's intensive talks at Leeds Castle in Kent to be chaired by the British and Irish governments.
There were indications last night that nationalists believe the two governments could use the September talks to assess whether the DUP and Sinn Féin are prepared to conclude a deal with each other which would enable a restoration of the Executive and the transfer of policing and justice powers.
Sources contacted by the Irish Times increasingly expect that the talks may not achieve a breakthrough, but could make sufficient progress for the process to be given more time.
However, this could mean that sensitive contacts between both sides would then risk running into a British general election which may be called next Spring.
Ulster Unionists, meanwhile, have stepped up their criticisms of the DUP, insisting the party is preparing to do a deal with republicans.
They argue this is tantamount to a U-turn which will see Sinn Féin ministers back in government in defiance of the DUP election promise to the contrary.