Hamas recently wrested legislative power from Abbas's long-ruling Fatah party, and is expected to form a cabinet within weeks.
In a related development, a top-level Hamas delegation is expected to arrive in Moscow next week for meetings with Russian officials.
Russia's invitation to Hamas has angered Israel. Hamas claimed responsibility for a string of suicide bombings in Israel and is sworn to the destruction of the Jewish state.
Israel, the United States, and the European Union consider Hamas a terrorist organization.