South Sudan's government and rebels sent delegates to peace talks in Ethiopia on Tuesday, Ethiopian officials said.
Rebel leader Riek Machar told the BBC he will enter peace talks, claiming his forces have captured the key town of Bor.
Machar previously demanded 11 detainees accused of being co-conspirators in the coup plan be freed before negotiations..
Militias loyal to former Vice President Riek Machar fought their way on Tuesday morning into the centre of Bor, the main town in the vast, underdeveloped Jonglei state and the site of an ethnic massacre in 1991, witnesses said.
Machar told the BBC his forces had taken the town while the army said it was outnumbered but still in control of several areas.
Uganda's president Yoweri Museveni has threatened the rebels with military action if they fail to agree to a ceasefire by the end of Tuesday, and begin talks.
In a BBC interview on Monday, President Kiir ruled out any power sharing with Mr Machar to halt violence that has killed at least 1,000 people in the last two weeks.
"What power sharing? It is not an option. This man has rebelled. If you want power, you don't rebel so that you are awarded with the power," Kiir said in an interview broadcast on the BBC Tuesday.
"You go through the process. When I came here I did not come through a military coup, I came because I was elected by the people."
Kiir, a former rebel commander, was elected president of South Sudan in 2011, just before the country became formally independent from Sudan.
"Elections are coming in 2015. Why did he not wait so that he goes through that same process?" Kiir added. "If he wins the elections, he then comes to this office."
"There can be no military solutions to any conflict, you try both military solutions and political solutions. Since day one I have said that I will resolve it by peaceful means," he added.
Regional leaders at the Inter-Governmental Authority on Development (IGAD) have demanded Machar hold face-to-face talks with Kiir by Tuesday.
Mr Machar told the BBC he was sending a delegation to Addis Ababa for peace talks, where he will discuss a ceasefire.
He also said his delegation will be led by Rebecca Nyandeng Garang, the widow of John Garang, who led South Sudanese rebel forces against Khartoum for many years.
The BBC's James Copnall in the capital, Juba, says as a Dinka she may help Mr Machar challenge the allegation that his rebellion is primarily from his Nuer ethnic group.
According to the AFP news agency, both parties are expected in the Ethiopian capital soon.
"Both President Salva Kiir and Dr Riek Machar are coming to Addis Ababa for talks, they are coming now and should meet today," Ethiopian foreign ministry spokesman Dina Mufti told the agency.