"The roadblocks may prove to be too great, but I firmly believe the diplomatic path must be tested," Obama said.
Obama acknowledged that Iranian President Hassan Rowhani, who plans to address the body Tuesday afternoon in New York, has signaled interest in charting a more "moderate" course and disavowed interest in pursuing the development of a nuclear weapon.
Saying the "conciliatory words" must be met by "actions," Obama said Kerry will "pursue this effort" to engage Iran, alongside representatives from the European Union and other global powers.
"We are determined to prevent Iran from developing a nuclear weapon," Obama said. He said the suspicion between the two countries can't be overcome overnight, but resolving the nuclear issue would be a "major step down a long road" toward a better relationship.
On the sidelines of the U.N. session, Kerry is expected to meet with his Iranian counterpart on Thursday, along with other diplomats. The meeting would mark the highest-level talks between the U.S. and Iran in decades.
Lawmakers on both sides of the aisle, though, have urged Obama to keep the pressure of sanctions on Iran and stand firm by the vow to prevent the country from developing a nuclear weapon. Sen. Marco Rubio, R-Fla., and several other senators penned a letter to Obama on Tuesday casting doubts on the intentions of Iran's new leader.
"Despite the hopes that many have had that Mr. (Rowhani) would dramatically improve Iran's abysmal human rights situation, Iranians still are being denied their fundamental freedoms of assembly, the press, and conscience," they wrote. On the nuclear issue, they said: "Despite sanctions and international pressure and the arrival of Mr. (Rowhani), Iran has not changed course and is close to obtaining this capability that will likely result in a cascade of nuclear proliferation in one of the world's most volatile regions."
They voiced concern that a deal with Iran might leave open the door to preserve part of its weapons program and access to the entire nuclear fuel cycle.
"Iran must not be allowed to retain any enrichment or reprocessing capabilities," they wrote. "Now is the time to increase pressure on Iran and to stand with the Iranian people, not pursue diplomatic half-measures that will allow their rulers to continue to delay and obfuscate and avoid real reforms."
The president addressed the General Assembly session amid a whirlwind of international developments.
The Obama administration recently backed off the threat of military force against the Assad regime in Syria, after his government agreed to a U.S.-Russia-backed plan for Damascus to turn over its chemical weapons to international control. Obama, though, still is seeking a tough resolution from the U.N. Security Council to enforce this pledge, and has said he'll keep the threat of military action on the table.
Earlier in his address, Obama called on the international community to "enforce the ban" on chemical weapons and make sure Syria's Assad regime lives up to its pledge to turn over its stockpile.
He called for a "strong Security Council resolution" to hold Bashar Assad accountable.
If the U.N. cannot agree to this, he said, "then it will show that the United Nations is incapable of enforcing even the most basic of international laws."
But a strong resolution, he said, would send a "powerful message" that chemical weapons have no place in the modern world.
Obama also spoke as the threat of Islamic terrorism once again reared its head, after an Al Qaeda-linked group stormed a shopping mall in Kenya, killing dozens of people. The stand-off with Kenyan security forces was still ongoing as the U.N. session got underway.
Earlier, U.N. Secretary-General Ban Ki-moon urged world leaders to stop fueling the bloodshed in Syria with weapons and get both sides to the negotiating table to end the "biggest challenge to peace and security in the world."
He called on the U.N. Security Council to adopt an "enforceable" resolution on the U.S.-Russian agreement to put Syria's chemical weapons under international control for future destruction and bring to justice the perpetrators of the Aug. 21 chemical weapons attack outside Damascus to justice "either through referral to the International Criminal Court or by other means consistent with international law."
U.N. diplomats say differences between the U.S. and Russia on how a resolution should be enforced have held up action in the Security Council. Russia is opposed to any mention of Chapter 7 of the U.N. Charter, which includes military and non-military actions to promote peace and security.
The secretary-general stressed that the international community "can hardly be satisfied with destroying chemical weapons while the wider war is still destroying Syria."
"The vast majority of the killing and atrocities have been carried out with conventional weapons," Ban said. "I appeal to all states to stop fueling the bloodshed and to end the arms flows to all parties."
The fighting in Syria has left more than 100,000 dead.