Salva Kiir told US Secretary of State John Kerry he had decided to sign after “a couple more days of consultation”, a State Department spokesman said.
His refusal on Monday to sign the deal to end an 18-month civil war was described as “mind-boggling” by the chief mediator.
The US said the latest developments were “encouraging”.
But it has submitted draft proposals for a UN arms embargo on South Sudan.
The UN Security Council blacklisted six generals – three from each side – in July, but member states were at the time unwilling to impose further sanctions.
Fighting between government and rebel forces resumed following Mr Kiir’s failure to endorse the deal on Monday.
Nearly two million people have been left homeless since conflict broke out in the world’s newest state in 2013.
Fighting erupted in that year after Mr Kiir accused rebel leader Riek Machar, his former deputy, of plotting a coup.
Mr Machar signed the accord in Ethiopia’s capital, Addis Ababa, on Monday – the deadline set by mediators.
Mr Kiir’s chief negotiator had said the deal was a sell-out that could not be implemented as the rebels were split.
But Seyoum Mesfin, a negotiator with the regional body Igad, told the BBC that all the government’s concerns had been addressed.
He said the UN and African Union would be asked to “take over” if Mr Kiir failed to sign in 15 days.
Rebel general James Koang Chuol said his troops had seized the key town of Pageri, near the border with Uganda, after beating back government forces, AFP news agency reports.
Fighting also took place in the Manyo district in oil-producing Upper Nile state, where government troops repulsed a heavy attack by rebels, army spokesman Philip Aguer told AFP.
The claims of both sides could not be independently verified.