"There is no legal government except for the Palestinian National Authority. Hamas are not representatives of a legitimate government, but coup-makers," Abbas said after crisis talks with Egyptian President Hosni Mubarak.
He said there would be no talks with Hamas until the group ends its coup, accepts international obligations, and holds elections.
A top Hamas member said in Egypt on Wednesday that the group is opposed to the involvement of third parties in running the Palestinian-Egyptian border.
A Hamas delegation crossed into Egypt through the Rafah border checkpoint en route to Cairo for talks with Egyptian officials.
"Egypt is our gate to the Arab, Islamic and entire world," Mahmoud Zahar was quoted by The Jerusalem Post as saying. "Therefore we will not allow the crossing to be used as a tool to suffocate the Palestinian people again."
He said the Hamas government is "the legitimate government that will not make any concessions on its legitimate acts."
A wall dividing Egypt and the Gaza town of Rafah was damaged by militants in a series of explosions on January 23. The border has yet to be sealed, and Palestinians continue to have free access to the Egyptian side. Thousands of Gaza residents, subjected to an Israeli embargo on goods and fuel, have used the opportunity to enter Egypt to buy much-needed supplies.
Hamas has said it may prevent Egypt from sealing the border unless the group's authority is recognized by Cairo.
