Benedict called for "a deeper search for ways of pre-empting and managing conflicts by exploring every possible diplomatic avenue, and giving attention and encouragement to even the faintest sign of dialogue or desire for reconciliation".
Speaking in French and English, the pontiff gave a wide-ranging address on issues such as globalisation, human rights and the environment.
"Every state has the primary duty to protect its own population from grave and sustained violations of human rights," the 81-year-old pontiff said.
"The promotion of human rights remains the most effective strategy for eliminating inequalities between countries and social groups, and increasing security," he added.
Before the pontiff's speech, Benedict held a private meeting with Ban Ki-moon, the UN secretary-general.
The Pope's New York visit will also include a visit to the site of the September 11, 2001, attacks.
The pope is on a six-day visit to the US that has been dominated by the issue of sexual abuse by Catholic priests in the US.
The trip is the first by a pontiff since a wave of abuse scandals began in 2002, provoking legal actions that led to more than $2bn in settlements.
On Thursday in Washington DC, Benedict prayed with weeping victims of childhood sexual abuse by priests.
Benedict earlier acknowledged at an open air mass in Washington that the scandal had sometimes been "very badly handled" by the church.
"No words of mine can describe the pain and the harm inflicted by the sexual abuse of minors," he told the congregation.
"Nor can I adequately describe the damage that has occurred within the community of the church."