GAZA, Jan 20 (Nidal al-Mughrabi/Reuters) - The Palestinian Islamist movement Hamas urged President Mahmoud Abbas on Friday to suspend exploratory peace talks with Israel following Israel's arrest of two Hamas legislators, and to stop his cooperation on West Bank security with the Israelis.

Hamas' Gaza Strip leader Ismail Haniyeh, recently back from a tour of Arab states, praised the rise of the Islamist Muslim Brotherhood in the Arab world and predicted black days for Israel because the nations know their path now.

Israeli soldiers on Thursday arrested senior Hamas official Aziz Dweik, speaker of the Palestinian parliament, on suspicion of involvement with terrorist groups, and detained another lawmaker of the group from Bethlehem, Khaled Tafish.

Hamas said Dweik was taken into custody at a checkpoint near the city of Ramallah. It accused Israel of trying to undermine moves by Abbas and Hamas leader-in-exile Khaled Meshaal to end four years of bitter rivalry and unite the two main Palestinian factions.

Haniyeh, speaking at a Gaza mosque after Friday prayers, said Abbas should call off meetings with Israeli negotiators in Jordan which are aimed at reviving peace negotiations suspended 15 months ago.

The pointless and failed meetings should stop. These failed experiences should stop, he said. A Palestinian should not shake the hand of his enemy, the enemy who arrests the symbols of Palestinian legitimacy.

We want to see something in the West Bank. We want to see the prisoners freed. We want to see the security coordination with the (Israeli) occupation stopped, Haniyeh said.

Palestinian reconciliation and security cooperation with the occupation are two parallel lines that cannot meet.

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Hamas seized control of the Gaza Strip from forces loyal to Abbas' Fatah movement during a brief civil war in 2007. The Palestinian legislative council has been effectively mothballed ever since.

Hamas and Fatah agreed to bury the hatchet and end their hostility with a reconciliation deal last year, but it has yet to be implemented in deed or in spirit.

Israel, the United States and the European Union consider Hamas a terrorist group opposed to peace and committed to violence to destroy what it calls the Zionist entity. Israel has warned that a Palestinian unity government which includes Hamas would end peace hopes.

Hamas deputy speaker Ahmed Bahar said Israel's detention of Dweik was intended to prevent Palestinian unity.

What happened requires Mr Mahmoud Abbas to declare an immediate stop to the negotiations in Amman in respect of our people and in respect of the parliament and its head, Bahar told reporters in Gaza.

It should be a firm message to the occupation that their continued crimes will not be give cover by the Palestinian Authority and will not pass without a response, Bahar said.

There was no immediate comment from Abbas's office. (Reporting by Nidal Almughrabi. Editing by Douglas Hamilton and Tim Pearce)