Former southern rebels in Sudan have suspended their involvement in the national unity government.
Mr Kiir, Sudan's vice-president, has warned of a return to war
The Sudan People's Liberation Movement (SPLM) said its northern partners had failed to implement parts of a 2005 deal that ended a 21-year civil war.
These include boundary demarcations and the redeployment of northern troops from the south.
South Sudan's President Salva Kiir warned recently there could be a return to war if the deal was not kept to.
Some 1.5 million people died in the conflict - Africa's longest civil war - which pitted the mainly Muslim north against the Animist and Christian south before the comprehensive peace agreement (CPA) was agreed.
So far the only government response has come from the spokesman at Sudan's London embassy, who said he was disappointed at the development but it was not a death blow to the CPA.
"It is a suspension, not a withdrawal as earlier reported by some news agencies," Khalid Al Mubarak told the BBC's Focus on Africa programme
"It is a suspension which is temporary and, pending discussions, hopefully this cloud will disappear."
"The leadership, the political group and our chairman called the advisers and the ministers and the state ministers to our headquarters in Juba and they are going to be there until we resolve the contentious issues," Yasir Arman, deputy SPLM secretary general, told the BBC.
The BBC's Amber Henshaw in the capital, Khartoum, says the Comprehensive Peace Deal (CPA) signed two years ago has been looking increasingly fragile over the last few weeks as importantant deadlines have been missed.
Mr Arman said the CPA had been violated in several ways and the north's National Congress Party had disregarded the wishes of SPLM leader Mr Kiir, who is also the country's vice-president.
"They are not consulting Mr Kiir; they are not consulting our ministers; they are taking many decisions - including expelling the representatives of the (UN) secretary general and different diplomats in Khartoum - without taking the opinion of the SPLM into consideration."
US envoy to Sudan Andrew Natsios said there was a real possibility of a return to conflict.
"This is one more step in this sequence of events, and what I am concerned about is that both the southerners and the northerners may make miscalculations about each others' intentions," he told the BBC's Newshour programme.
"One thing we are worried about is that the senior political leadership in the north and the south maintain control over their field commanders."
The power and wealth-sharing deal is intended to pave the way for elections by 2009 and to give the south the right to decide whether to split from the north by 2011.
Correspondents say there is not yet an agreement on the final border between north and south which means the division of oil wealth cannot be completed.
According to an SPLM statement, the party is also unhappy that its request to reshuffle its ministers in the coalition government has been ignored.
Currently there are 10,000 UN peacekeepers in southern Sudan.