US President Barack Obama said Tuesday he is ready to test a difficult "diplomatic path" to better relations with Iran while pressing for an end to its nuclear drive.

Speaking just ahead of Iran's new president Hassan Rowhani, Obama devoted much of his speech to the UN summit to overtures to the new Tehran leadership.

Obama said "Iran's pursuit of nuclear weapons" would remain a US foreign policy priority and stressed that "mistrust has deep roots" between the United States and Iran.

But he added that a "meaningful agreement" between the arch-rivals is possible.

The United States ended diplomatic relations with Iran in 1980 in the stormy aftermath of the Islamic Revolution. Rivalry has heightened since then, with the United States leading the sanctions drive over western accusations that Iran is trying to develop a nuclear bomb. Tehran denies it seeks a bomb.

"I don't believe this difficult history can be overcome overnight -- the suspicion runs too deep. But I do believe that if we can resolve the issue of Iran's nuclear program, that can serve as a major step down a long road towards a different relationship -- one based on mutual interests and mutual respect."

Obama said he had written to Iran's Supreme Leader Ayatollah Ali Khamenei and Rowhani saying that the United States was "determined to prevent them from developing a nuclear weapon" but that it did not want "regime change".

Noting that Rowhani has said Iran will "never" build a nuclear bomb, Obama said there was a basis for "a meaningful agreement."

"To succeed, conciliatory words will have to be matched by actions that are transparent and verifiable" on the nuclear program.

"The roadblocks may prove to be too great, but I firmly believe the diplomatic path must be tested," Obama said.

Rowhani did not attend a lunch for world leaders given by UN leader Ban Ki-moon where he could have met Obama. Iran said a meeting with Obama was not on Rowhani's "agenda."

But Rowhani did meet French President Francois Hollande. In his speech to the assembly Hollande also said that Iran must take "concrete" measures on its nuclear program to reassure the international community.

Syria dominated speeches on the first day of the assembly, however, and Obama said Syrian President Bashar al-Assad must face "consequences" if he fails to hand over his chemical weapons.

Obama insisted the United States is ready to use military force to protect its "core interests" in the Middle East. And he renewed a demand that the UN Security Council pass a "strong" resolution backing a Russia-US plan to destroy Assad's chemical weapons.

Hollande said a resolution being negotiated by the Security Council must allow for eventual "coercive" measures against Assad if he does not keep to the disarmament plan.

Russia has been resisting attempts to make the disarmament plan mandatory under Chapter VII of the UN Charter. Chapter VII can also be used to justify eventual military force and Russia has fiercely rejected any move toward approving a military strike.

The United States had threatened a military strike against Assad's forces over an August 21 chemical attack near Damascus, which the United States says killed some 1,400 people.

Russia's Foreign Minister Sergei Lavrov was in the hall to hear Obama's speech and was to hold talks with US Secretary of State John Kerry later Tuesday.

UN Secretary-General Ban Ki-moon called on all states to stop sending weapons to Syria.

"I appeal to all states to stop fuelling the bloodshed and to end the arms flows to all parties," Ban said as he opened the UN summit, which is being attended by more than 130 heads of state and government.

Russia is Assad's key arms provider while Syria accuses Saudi Arabia, Qatar and other Gulf states of arming opposition rebels.

Brazil's President Dilma Rousseff used her speech ahead of Obama to launch a blistering attack on the United States for spying on her country.

"The argument that illegal interception of information is allegedly intended to protect nations against terrorism is untenable," Rousseff told the assembly, though Obama was not present.

"Brazil knows how to protect itself," she added.

Rousseff cancelled a long planned state visit to the United States next month in anger at revelations leaked by fugitive former CIA employee Edward Snowden that the National Security Agency had spied on her email.

The spy revelations have "brought anger and repudiation among vast sectors worldwide," Rousseff said.

Obama insisted that while the United States was now reviewing its intelligence gathering, it had proved invaluable in the fight against terrorism.