UNITED NATIONS (AP) -- Iranian President Hassan Rouhani called the United States a "great" nation Friday in a sharp reversal from his predecessors and expressed hope that at the very least the two governments can stop the escalation of tensions.

Wrapping up his first trip to the United States as Iran's new leader, Rouhani said President Barack Obama struck a new tone in his U.N. speech this week, which he welcomed.

He said he believes the first step to a meeting between the two leaders was taken Thursday at a meeting on Iran's nuclear program, where the foreign ministers of both nations talked for the first time in six years. The White House announced Friday afternoon that Rouhani and Obama spoke on the phone.

"I want it to be the case that this trip will be a first step, and a beginning for better and constructive relations with countries of the world as well as a first step for a better relationship between the two great nations of Iran and the United States of America," Rouhani told a press conference at a hotel near U.N. headquarters.

Iran and the United States have traded harsh rhetoric for years.

During the 1979 Iranian revolution, Ayatollah Ruhollah Khomeini returned from exile, seized power and declared the U.S., which was a strong supporter of the ousted Shah of Iran, the "Great Satan." He set the tone for Iranian officials who came after him. The U.S. was equally critical, with then-President George W. Bush, in his 2002 State of the Union address, declaring Iran part of his "axis of evil" along with North Korea and Iraq.

Rouhani, looking to the future of U.S.-Iranian relations, expressed hope that "the views of our people, the understanding of each other, will grow, and at the level of the two governments that at the very least we can, as a first step, stop further escalation of tensions and then reduce tension as a next step and then pave the way for achieving of mutual interests."

The Iranian president was upbeat about his four-day visit to New York to attend the U.N. General Assembly's ministerial session, reeling off a long list of leaders he met and saying "I believe that our success was greater than our expectation, especially with the European countries ... and I think that the path really has been paved to expand relations in various centers, key world economies."

Iran's economy has been hit hard by four rounds of U.N. sanctions for its failure to suspend uranium enrichment, a process that can be used to make fuel for both nuclear weapons and nuclear energy. The U.S. and its allies have taken even more devastating measures targeting Iran's ability to conduct international bank transfers and to export oil.

Rouhani has come across as a more moderate face of the hard-line clerical regime in Tehran. He said he has a mandate from the Iranian people, who opposed "extremism" and voted for "moderation." He said this has created a "new environment" that could pave the way for better relations with the West.

He said Iran would put forth a proposal at talks in Geneva on Oct. 15-16 aimed at resolving the standoff over his country's nuclear program and easing international sanctions.

"We hope that an even more effective step will be taken in Geneva in order to settle the nuclear issue," Rouhani said, without elaborating.

He expressed hope that with "sufficient will on both sides - and I assure you that on the Iranian side this will is there fully, 100 percent - that within a very short time there will be a settlement on the nuclear file and ... I believe that in the not too distant future, we'll be able to resolve and settle the nuclear issue."

Resolving the nuclear issue will "pave the way for Iran's better relations with the West," including the expansion of economic and cultural ties, he said.

Rouhani said he was encouraged by what he has heard recently from Western officials.

"In speaking with senior European officials and also hearing Mr. Obama ... it seemed that they sounded different compared to the past, and I view that as a positive step to the resettlement of the differences between the Islamic Republic between the Republic of Iran and the West," he said.

He said he did not meet with Obama on the sidelines of the U.N. General Assembly this week because "both sides were convinced that the timetable was too short to plan a meeting of two presidents" and "ensure that its conclusion would be solid."

"What matters to us is the result of such a meeting," Rouhani said.

Iran watchers say Rouhani may have limited time - possibly a year or less - to reach a settlement on the nuclear issue before Iran's Supreme Leader Ayatollah Ali Khamenei decides negotiations are fruitless.

In an apparent reference to resistance among hard-liners back home, Rouhani noted that "after 35 years of great tensions between Iran and the United States and a very number of issues that persist ... a meeting of the presidents for the first time will naturally come with complications of its own."

He said the first step was the ministerial meeting Thursday, and the next steps have to be taken in stages in "a well-thought-out manner."

The upbeat, if guarded, tone by both sides after Thursday's meeting of Iran, the five permanent members of the U.N. Security Council and Germany was seen as a significant step forward after months of stalled talks. It was capped by an unexpected one-on-one meeting between U.S. Secretary of State John Kerry and Iranian Foreign Minister Mohammad Javad Zarif, who shook hands and at one point sat side-by-side in the group talks.

On other issues, Rouhani condemned the use of chemical weapons in Syria, welcomed President Bashar Assad's decision to join the Chemical Weapons Convention, and said Iran will actively participate in a new Syrian peace conference if invited.

He said the international community must show "deep sensitivity" to the presence of al-Qaida and other terrorists in Syria, saying "terrorists are like bacteria that travel constantly from one setting to another."

He also said that there's no room in the world today for the extreme practices of the Taliban, who curtailed human rights and barred girls from going to school when they were in power.

"Women are like men and equal with me and must be fully active in the social sphere," Rouhani said.

He expressed hope that the Taliban would re-emerge with new thinking and beliefs to participate in a future framework for peace for Afghanistan.

In Vienna, meanwhile, Iranian and U.N. officials held a "constructive" meeting on resuming a probe of allegations that Tehran has worked on atomic arms, officials said Friday, in talks seen as a test of pledges by Rouhani to reduce nuclear tensions.

The upbeat assessment and an agreement to meet again Oct. 28 was a departure from the deadlock left by previous meetings over nearly two years.

At issue are suspicions outlined in reports from the U.N.'s International Atomic Energy Agency that Iran worked secretly on trying to develop nuclear weapons - something Tehran denies.

Rouhani has steadfastly maintained that any nuclear agreement must recognize Iran's right under international treaties to continue enriching uranium