Kerry, on his second visit to Kabul within weeks, set a target for the new president to be in office by the end of this month despite a dispute between Ashraf Ghani and Abdullah Abdullah over alleged electoral fraud.
The threat of political chaos looms large in Afghanistan after Abdullah refused to accept a preliminary vote count that put Ghani ahead, saying that the election had been stolen by massive ballot-box stuffing.
The deal was seen as a breakthrough as tensions spiked between candidates' supporters and the United Nations warned of the risk of a return to the ethnic violence of the 1990s civil war.
But the two candidates have since clashed repeatedly over both the audit and the power-sharing plan, with little sign that either side is prepared to concede defeat.
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The summit is scheduled to sign off on a US-led "training and advisory" mission in Afghanistan next year after all foreign combat troops withdraw by December.
But NATO nations have expressed reluctance to make costly commitments if the country fails to complete its first democratic transfer of power -- a key goal of the massive international military and aid effort since 2001.
"We would like to see the inauguration ideally by the end of the month," said a US official travelling with Kerry.
Kerry told Abdullah today he had been up late working on the US decision on possible air strikes in Iraq, where the Yazidi religious minority is besieged by Sunni extremist fighters.
US President Barack Obama said the strikes were necessary to prevent a "genocide" by Islamic State militants who have seized swathes of Iraq's northern and western regions.
Today morning, Kerry met with outgoing Afghan President Hamid Karzai, who has also called for the delayed inauguration of his successor to be held within weeks.
Taliban insurgents have launched new operations in the south and east in recent months, and violence is increasing across the country according to several independent reports.