Carter, who is monitoring the election process, met with Dahal in the evening, but their aides would not discuss details.
In an earlier interview, Carter said his advice to Dahal and the Maoist party would be "that if they have differences of opinion about whether the election was honest or fair, to take their complaints in an orderly way to the election commission, and then to the judiciary if necessary, and not resort to any sort of violence and so forth. And do it peacefully according to the procedures that this country has adopted."
He said the election was well conducted, honest, fair and peaceful as well.
"Boxes were brought to central counting places in a honest and fair and very highly carefully supervised way and we witnessed 31 different counting centers and (they were) very careful and meticulous the way they were doing it," he said.
Chief Election Commissioner Neel Kantha Upreti said there were no plans to stop the vote counting.
Initial results showed Nepali Congress party and Communist Party of Nepal (United Marxist-Leninist) had won eight seats each in the 601-member Constituent Assembly that would double as the parliament. Final election results will take at least a week. None is predicted to win a majority, making a coalition government likely.
The Maoists are former communist rebels who fought government troops between 1996 and 2006. They gave up their armed revolt, joined a peace process and mainstream politics, and their fighters have joined the national army.
Political leaders in the last assembly disagreed over who got to lead the nation and on creating a federal system divided by ethnic groups or by geography. The resulting power vacuum has left Nepal without a proper constitution for nearly seven years.