Hamas spokesman Hasan Yusuf said in a statement - a copy of which was obtained by Aljazeera - that the movement expected Annan to take a responsible stance that rejected the idea of the separation wall and to support the decision issued by the International Court of Justice to this effect.
UN chief Annan, on his first visit to the Middle East in four years, vowed on Monday that the world would push ahead with the peace process after talks with Palestinian Authority President Mahmud Abbas.
But he did not discuss the issue of the separation barrier - a crucial point to the Palestinians - except to say, when asked by reporters, that the UN would "stand by the decision of the General Assembly and the Security Council".
While he was inside the Muqata, the Palestinian government compound in Ram Allah, about 500 demonstrators gathered outside to denounce Israel's controversial West Bank wall, which they see as a land grab, and the UN stance.
"The aim of this demonstration is to send a message to Annan that he didn't do his duty very well. It's forbidden to implement the UN decision on Lebanon and not here in Palestine," said Mustafa al-Barghuthi, the unofficial Palestinian opposition leader.
"Annan's duty must include implementing The Hague's decision"
Mustafa al-Barghuthi, unofficial Palestinian opposition leader
"Annan's duty must include implementing The Hague's decision," he added.
Protesters held up banners saying: "We must fight the wall until it falls" and: "Implement the ICJ decision and stop the wall."
Last July, the ICJ in The Hague ruled that the barrier, which often cuts deep into Palestinian territory, is illegal, but Israel has vowed to complete building it anyway.