Abbas earlier said the lineup of a unity government will be announced Monday, after a delay over who will head the foreign ministry.
The Islamist movement Hamas and the Western-backed Palestine Liberation Organisation, dominated by Abbas's secular Fatah party, signed a surprise reconciliation agreement in April to end years of rivalry.
During his telephone call with Abbas on Sunday, Kerry "expressed concern about Hamas's role in any such government and the importance that the new government commit to the principles of nonviolence, recognition of the state of Israel and acceptance of previous agreements with it," State Department spokeswoman Jen Psaki said.
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"President Abbas assured the secretary that the new government would be committed to these principles."
Kerry stressed that the United States would "judge any government based on its composition, policies, and actions," Psaki added in a statement.
On Saturday, Abbas also said the ministers in the new lineup would not come from either Farah or Hamas.