Merkel welcomed the results of the summit and said Europe should build on it and revive diplomatic efforts by the Quartet of Middle East power brokers, which includes the European Union, the United States, the United Nations and Russia.
"The new government should show signs of maturity and responsibility"
Husky, Ottawa, Canada
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Merkel, on Sunday at the Hebrew University of Jerusalem where she was given an honorary doctorate, said: "We all have the feeling that things are moving. We have a window of opportunity. There is a major chance here which we must grasp."
Aides said Merkel would not meet any ministers from the Palestinian unity government during her visit.
The government, led by the Hamas movement, includes members of Abbas's Fatah faction and independents.
Merkel met Olmert and Tzipi Livni, Israel's foreign minister, before touring the Yad Vashem Holocaust museum.
Olmert said: "Israel is at a critical crossroads of important decisions.
"We are in a process of confronting significant threats on the one hand and opportunities to advance the diplomatic process with Arab countries on the other."
During a visit to Jordan on Saturday, Merkel urged the Palestinian unity government to embrace the demands of the Quartet of Middle East mediators to recognise Israel, renounce violence and abide by existing peace accords.
She also wants to persuade the Palestinians to win the release of an Israeli soldier held in Gaza since last year.
The unity government's programme contains a promise to "respect" previous Israeli-Palestinian pacts but does not explicitly call for recognising Israel.
Mustafa Barghouti, the minister of information and unity government spokesman, has said the government renounces civilian violence but insists on a legitimate right to resist occupation under international law.
As EU president, Germany represents the 27-member bloc in the Quartet, which also includes the United States, the European Union, Russia and United Nations.
Fawzi Barhoum, a Hamas spokesman, said on Saturday the group "will never recognise the right of Israel to exist".
In a break with Israeli policy, European Union foreign ministers agreed on Saturday to engage with non-Hamas members of the unity government.
Olmert has vowed to shun the unity government, including non-Hamas ministers.
Merkel has made reviving the stalled peace process a priority but hopes for a breakthrough are low.
During her Middle East tour, Merkel will also visit Lebanon, meeting Fouad Siniora, the prime minister, and will tour a German frigate which is part of the UN peacekeeping mission there.