It comes after Malaysia launched a military assault in an attempt to end an incursion by a group of Filipinos who say the land belongs to them.
At least 27 people have been killed since the initially peaceful two-week stand-off erupted into violence.
On Wednesday, Malaysian troops hunting the Filipinos said they had found at least 13 bodies.
In a statement, Mr Ban’s office said he encouraged all sides to engage in dialogue to resolve the situation peacefully.
“The Secretary-General expresses concern about the impact this situation may have on the civilian population, including migrants in the region,” said the statement.
“He urges all parties to facilitate delivery of humanitarian assistance and act in full respect of international human rights norms and standards.”
The group of some 200 Filipinos landed at a coastal village in the Lahad Datu district of Sabah, on Malaysian Borneo, in mid-February, saying that the territory was theirs.
Calling themselves the Royal Army of Sulu, the clan members said they were descendants of the Sultanate of Sulu in the southern Philippines, which ruled parts of northern Borneo for centuries, and demanded that the Malaysian government pay more money to lease their land.
Initial attempts by both the Philippines and Malaysian government to persuade them to leave failed, and late last week, clashes broke out between the clan and Malaysian police, leaving eight policemen and 19 clansmen dead.
On Tuesday Malaysian troops backed by fighter jets raided the area around Tanduo, where the clan were holed up. On Wednesday they then carried out extensive searches of the area, saying some of the Filipinos could be hiding among the local population.
The clan said on Wednesday that none of its members had been killed, but later in the day, Malaysian officials displayed what they said were photographs of 13 bodies they had found in a shallow grave in Tanduo.
It was not clear whether they had died during the assault or in last week’s clashes.
Malaysian Defence Minister Zahid Hamidi said one of the bodies was a man who was shot in a firefight on Wednesday, and that more bodies could yet be found.
He said the security forces had not suffered new casualties since last week.
Both the Malaysian and Philippines governments are coming under increasing public pressure to end the ongoing crisis.
A rally was held in the Philippines capital, Manila, on Wednesday night calling for a peaceful resolution and expressing concern for the safety of the many Filipinos who live and work in Sabah.
“We are very apprehensive that it may get out of control,” Norhaya Nacusag told Reuters.
“We are united and firm in our call to both parties for the unconditional and immediate cessation of hostilities and for the Malaysian government and the Sulu Sultanate to immediately work for the de-escalation of conflict and to open up dialogues to resolve this conflict.”
The Manila-based leader of the Filipino clan, Jamalul Kiram III – one of several men who claims the title of Sultan of Sulu – said earlier this week they they were prepared to “fight to the last man”.