The Secretary-General is "concerned about the recent escalation of violence along the Line of Control between India and Pakistan.
He deplores the loss of lives and the displacement of civilians on both sides," a statement issued by Ban's spokesman said.
"Ban encourages the governments of India and Pakistan to resolve all differences through dialogue and to "engage constructively to find a long-term solution for peace and stability in Kashmir," it said.
A war of words between the two countries over the situation at the Line of Control took place on Tuesday at the UN General Assembly where India said that it was a "matter of deep regret" that Pakistan violated the ceasefire, in which eight people were killed and several others injured.
India made it clear that its armed forces are "fully ready" to respond to "provocation".
India also said that the onus of creating a positive environment for normalisation of relations is on Pakistan.
Eight civilians have been killed in India as Pakistan targeted dozens of army outposts and villages; more than 80 have been injured.
Pakistan says it has lost 11 civilians.