The talks are set to be the first in a series of what are due to be regular meetings between the two leaders after an agreement reached during a visit to the region by Condoleezza Rice, the US secretary of state last month.
Fawzi Barhoum, Hamas spokesman, dismissed the meeting as “useless” and a “photo opportunity”.
“Let us respect all religions, civilizations and people that were originated from the Middle East,….and let’s drive for respectable, long lasting and fair solution.”
While Dr Khalil Abu Leila, a Hamas leader in Gaza, told Al Jazeera that he did not expect positive results from the meeting.
“This meeting basically serves Israeli interests. I believe that Olmert wants to discuss security issues in the first place and then wants to strengthen his internal situation as his popularity inside ‘the Israeli entity’ is shaken.”
But Ephraim Sneh, Israeli deputy defence minister, said that just the agreement to meet in itself was important.
“When the alternative is to do nothing, even the the tiniest amount of progress towards negotiation on a permanent accord is welcome,” he told Israeli Army Radio.
Palestinian groups have given Israel, through Egyptian mediators, a list of Palestinian prisoners that they want released in exchange for freeing Gilad Shalit, an Israeli soldier captured in June.
“This is a topic which will not be removed from our agenda,” Olmert said on Sunday, referring to the captured reservist.
Ahead of the meeting, Olmert told his weekly cabinet meeting that Israel was ready to talk to Arab nations about their peace plan for the region.
“We are ready to hold talks with any combination of Arab states on their ideas and I would be glad to hear their ideas on the Saudi initiative,” he said.
“I’ll be glad to hear their ideas and for them to listen to ours,” he added. “I hope there will be a chance for such meetings.”
An Arab League summit last month revived a proposal which offers Israel peace and normal ties with Arab countries in exchange for withdrawing from land occupied during the 1967 Six Day War, allowing the creation of a Palestinian state and the return of refugees.
Israel, which initially rejected the plan when it was first unveiled in 2002, has said recently it could provide a basis for talks, provided there are amendments to the refugee issue – something the Arab states have refused.
An Arab League committee of 13 foreign ministers will meet in Cairo on Wednesday to talk about setting up several working groups to promote the 2002 Arab initiative.