In his conversation with Prime Minister Ehud Olmert, Ban also expressed concern over Israel's excavation in east Jerusalem, which has been widely condemned by Arab and Muslim governments, spokeswoman Michele Montas said.
Ban, a member of the quartet of Middle East advisers, spoke to Olmert, Palestinian President Mahmoud Abbas and Saudi King Abdullah over the weekend.
Hamas has rejected the Quartet's conditions for restoring Western aid: recognition of Israel, renunciation of violence and acceptance of existing interim peace agreements.
Hamas, which came to power in March 2006 after winning Palestinian elections, and Abbas' long-dominant Fatah faction signed an agreement in Mecca, Saudi Arabia, on Thursday to from a unity government. The agreement made no explicit commitment to recognize Israel.
The Quartet, which includes the United States, Russia, the European Union and the United Nations, advocates a faltering road map aimed at securing a two-state solution to the Middle East conflict. Ban plans to go to Berlin for a Quartet meeting on February 21.
Montas said Ban had relayed to Olmert the protests of Arab ambassadors, who had asked him to intervene over the East Jerusalem excavations.
Arab nations fear the work, which began last week, could damage the foundations of the 1400-year-old al-Aqsa Mosque. Israel says the excavations aim to salvage artifacts before construction of a pedestrian bridge leading to the complex, and would do no harm.
On Friday, some 200 Israeli police wielding batons stormed protesters who threw stones at them at the plaza outside al-Aqsa Mosque. Seventeen protesters and 15 police officers were injured.