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The rivalry between Abbas and Hamas is bitter and often violent, and Abbas has repeatedly said he would have no contact with Hamas until it cedes power in Gaza.
Israel has said that if Abbas renews ties with the Islamic group, which remains openly committed to Israel's destruction, it will break off peace talks with the Palestinians.
The meeting followed on Friday prayers at Abbas' presidential compound and was attended by four Hamas members, including Nasser al-Shaer, who was deputy prime minister in the Hamas-led unity government that broke apart after the Gaza takeover in June.
Al-Shaer said the group discussed "internal affairs in an open atmosphere" with Abbas, but added that the visit was "not a meeting between Hamas and the President." Abbas' office also denied that the meeting was official or that the Hamas men had been invited.
However one of the Hamas men, Hussein Abu Quaik, said they had been invited to prayers by Abbas.
"Everybody in Hamas knew about this,' Abu Quaik said. "This will contribute to strengthening our relationship, and lay the basis for national unity, God willing.''
Israeli government spokesman David Baer said Israel objected to any contacts with Hamas.
"It's Israel's position that Hamas should be sidelined and kept out of the game until it accepts the conditions placed upon it by the international community," Baker said. - DDNEWS