The two met in an upscale hotel for what US officials have billed as "informal" talks, seeking to downplay any hopes of a breakthrough in Kerry's ill-fated bid to reach an Israeli-Palestinian peace deal.
"The door remains open to the peace process. The secretary continues to believe that. But the purpose of the meeting is more about our ongoing relationship with the Palestinian people," a senior State Department official said before Kerry left Washington.
Washington has branded Hamas a terrorist organisation since 1993 and has said it must recognise Israel and renounce violence.
Top US officials have already warned that any Palestinian government which includes members of Hamas would risk a freeze in hundreds of millions of dollars of US funding to the Palestinian Authority.
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But the April 29 deadline expired with the peace process in disarray, forcing Kerry and his team to declare a "pause" in the negotiations.
Abbas met earlier Monday with British Prime Minister David Cameron.
"President Abbas outlined his plans for a new, technocratic Palestinian government, committed to the Quartet principles, including non-violence and the recognition of Israel," a Downing Street spokesman said.
Cameron had urged Abbas to make "progress towards securing the rapid resumption of peace talks, which remain the only viable route to a lasting solution.