President Kiir refused to sign the peace deal because the reinstated clauses would see the capital Juba declared a demilitarised zone, have him share power with Mr Machar both at the national and state level, and exercise executive authority with his rival.
Perhaps most controversially, the peace deal would allow Mr Machar to be in control of his rebel forces while Mr Kiir would be in charge of the national army – presenting a dangerous situation where the country could potentially have two commanders-in-chief.
A recent meeting in Entebbe, Uganda, bringing together the so called “frontline” states, resolved to remove these provisions.
Mr Kiir’s chief negotiator said the deal was a sell-out that could not be implemented as the rebels are split.
The deadline for a peace deal expired on Monday night, and South Sudan’s warring parties may now face international sanctions.
According to mediators at the talks, Kiir did not sign the agreement and asked for 15 days to consult with his constituencies.
The decision is seen as the latest blow to peace talks sponsored by the East African bloc IGAD, the Intergovernmental Authority on Development, as well as several other countries, including the United States and China.
Tens of thousands have died and more than two million have been displaced since fighting broke out in the young state in 2013.
The sides traded accusations about who was responsible for an attack in the town of Pageri, near the border with Uganda, early on Tuesday.
Military spokesman Philip Aguer said rebel accusations were “lies” and blamed them.
At Monday’s summit in Ethiopia attended by regional powers and international mediators, South Sudan’s government initialled a draft agreement, but requested a further 15 days before signing in full. Mr Machar did sign it.
UN Secretary-General Ban Ki-moon urged Salva Kiir to sign up and cease hostilities, saying he was “deeply pained by the horrendous suffering of South Sudanese civilians”.
The US was “deeply disappointed” that President Kiir’s government had “yet again squandered” an opportunity to bring peace by refusing to sign the agreement, a statement from US National Security Adviser Susan Rice said.
“The US deplores this failure of leadership,” it added.