In his conversation with Prime Minister Ehud Olmert, Ban also expressed concern over Israel's excavations 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 Authority Chairman Mahmoud Abbas and Saudi King Abdullah over the weekend.
Also Monday, Palestinian Prime Minister Ismail Haniyeh appealed to the international community to honor the unity deal signed by warring Palestinian factions last week and to lift economic sanctions on the Palestinian Authority.
Today there is a cautious, pessimistic U.S. position towards this agreement," said Haniyeh. "I say to the Quartet and to the European Union that this is the will of the Palestinian people, and they should respect it and they should work to end the status of siege," he said.
Senior Palestinian officials said Monday they will start forming a new, national unity government in coming days, but acknowledged that previous dealbreakers, such as control over the security forces and the fate of Hamas' militia, have still not been resolved.
Under the power-sharing deal reached last week in Mecca, Saudi Arabia, the Hamas-led cabinet is to step down in the coming days, to make way for a unity government with Abbas' rival Fatah movement.
The two sides have agreed to a division of ministerial posts, but have not yet reached agreement on the names of most of the government ministers.
One unresolved issue is who will be interior minister and thus exert considerable control over the security forces. Wrangling over such control helped spark deadly Hamas-Fatah clashes in Gaza in recent months.
The deal also did not settle the fate of Hamas' 5,600-strong militia, which was formed last year over Abbas' objections. Under one proposal, the force would be dismantled and its members assigned to various security branches, as part of an overall reform of the security forces, who are mainly loyal to Abbas.
"When President Abu Mazen comes to Gaza, we will continue the negotiations on issues that remain," Haniyeh said an address on Palestinian television.
Haniyeh, of Hamas, returned to Gaza on Monday and said his government planned to resign in the coming days to start the process of forming the new coalition.
"We are convinced of the necessity of speeding up the resignation to within days, possibly Wednesday, Thursday or Friday," Haniyeh told reporters at the Egypt-Gaza border crossing.
Under the Mecca deal, Hamas is to propose candidates for interior minister, and Abbas has the right to choose one of them. Haniyeh said Monday that Hamas has proposed two candidates, but has not yet heard back from Abbas.
Haniyeh, who has five weeks to put together a government, is to meet with Abbas on Thursday. Two key portfolios, foreign and finance, have already been assigned to independents.
Once the Hamas government resigns, Abbas would send a letter of designation for a new coalition, to be headed by Haniyeh, said Abbas aide Rafiq Husseini.
The PA chairman "wants to move quickly and hopes to issue the letter within days," Husseini said.
Abbas is also trying to win international support for the coalition deal, even though it falls short of international demands that any Palestinian government recognize Israel and renounce violence.
The Mecca deal says the coalition would respect all agreements signed by the PLO, including those with Israel, but does not specifically recognize Israel's right to exist.
"The agreement moves in the direction of the international community's demands," Husseini said. "We hope the international community will look at the agreement from a positive side," he added.
Palestinian officials hoped the deal would lead to a lifting of international sanctions that were imposed after Hamas' election last year.
But foreign governments said they would wait to study the agreement and to see if the new government had the will - or ability - to prevent ongoing attacks on Israel, including rocket attacks from the Gaza Strip.
On Monday, Gaza militants launched five rockets into Israel, causing no injuries, the army said.
On Tuesday, Abbas is meeting in Jordan with Russian President Vladmir Putin. Russia is one of the members of the "Quartet" of Middle East peace brokers, along with the U.S., the European Union and the United Nations.