"The final result will be less important, however, than the way the contest is decided," the group added. "Such periods of transition are a crucial test for a country's institutions. This is a moment when Afghans must hold tight to their constitution and the rule of law, despite political turmoil."
After Saturday's meetings in Kabul, Kerry is expected to travel to Vienna, Austria, for talks on Iran's nuclear program.
Iran and six world powers, the United States among them, are engaged in a final round of negotiations ahead of a July 20 deadline aimed at reaching a permanent deal on the future of Tehran's nuclear program.
Tehran insists its ambitions are peaceful, but the world powers fear it has ambitions to build nuclear weapons.
Kerry is due to speak in Vienna with his German counterpart Frank-Walter Steinmeier, the senior administration officials said. The foreign ministers' encounter will come amid a row over fresh spying allegations against the United States.
Germany's government on Thursday asked America's top spy chief stationed in the country to leave.
This followed the revelation that two Germans -- one working at a German intelligence agency, the other in the Ministry of Defense -- are suspected of spying for the United States.