The call came one day after Secretary of State John Kerry and the other members of the P5-plus-1 (the five permanent members of the U.N. Security Council plus Germany) met with Iranian Foreign Minister Javad Zarif on the margins of the U.N. General Assembly in New York.
Hopes Obama and Iranian President Hassan Rouhani would meet at the United Nations were dashed Tuesday after those trying to arrange an encounter said it was too complicated.
In his Friday afternoon statement, Obama said he is confident an agreement on Iran's nuclear program can be reached.
"I reiterated to President Rouhani what I said in New York -- while there will surely be important obstacles to moving forward, and success is by no means guaranteed, I believe we can reach a comprehensive solution," Obama said, adding he has directed Kerry to pursue negotiations.
"Resolving this issue, obviously, could also serve as a major step forward in a new relationship between the United States and the Islamic Republic of Iran -- one based on mutual interests and mutual respect. ...
"A path to a meaningful agreement will be difficult, and at this point, both sides have significant concerns that will have to be overcome. But I believe we've got a responsibility to pursue diplomacy, and that we have a unique opportunity to make progress with the new leadership in Tehran."
Iran is hoping the West will ease sanctions that have crippled its economy. The sanctions were imposed to try to keep Iran from developing a nuclear weapon.
Catherine Ashton -- EU foreign affairs and security policy representative -- said talks among the nations this week have been "substantial" and all parties have agreed to "go forward with an ambitious timeframe," Sky News reported Friday.
Ashton said senior negotiators have scheduled meetings for Oct. 15-16 in Geneva, Switzerland.
After top U.S. and Iranian diplomats met this week for the first time in more than 30 years, Kerry said he and Zarif discussed the possibility of how to proceed based on President Barack Obama's speech to the U.N. General Assembly concerning Iran's nuclear program.
"We had a constructive meeting, and I think all of us were pleased that Foreign Minister Zarif came and made a presentation to us, which was very different in tone and very different in the vision that he held out with respect to possibilities of the future," Kerry said of his one-on-one meeting Thursday with the Iranian official at United Nations headquarters in New York.
"Needless to say, one meeting and a change in tone, which was welcome, doesn't answer those questions yet, and there's a lot of work to be done," Kerry said. "So we will engage in that work, obviously, and we hope very, very much -- all of us -- that we can get concrete results that will answer the outstanding questions regarding the program."
Iran maintains its nuclear program is solely for civilian purposes but intelligence agencies and international inspectors have said it appears to have a military dimension as well.
Zarif "put some possibilities" on the table during their discussion, Kerry said.
"Now it's up to people to do the hard work of trying to fill out what those possibilities could do," he said.
Zarif also called the meeting "constructive," CNN reported.
"We hope to be able to make progress towards resolving this issue in a timely fashion based on respecting the rights of the Iranian people to nuclear technology for peaceful purposes, including enrichment. And, at the same time, making sure that there is no concern at the international level that Iran's nuclear program is anything but peaceful," Zarif told reporters after the meeting.
Zarif gave a 15- to 20-minute presentation to a group of diplomats Thursday, laying out Iran's interests and desire to strike an agreement with other nations that would be fully implemented within a year, a senior State Department official told CNN.
The Kerry-Zarif session was the first high-level bilateral meeting between the United States and Iran since New Year's Eve in 1977 when President Jimmy Carter met the shah of Iran.
"We stressed the need to continue these discussions to give it the political impetus that it requires, and hopefully to reach a conclusion in a reasonable time," Zarif said. "I'm satisfied with this first step. Now we have to see whether we can match our positive words with serious deeds so that we can move forward."
Kerry and Zarif met first in the U.N. Security Council's consultation chamber along with foreign ministers from Britain, France, Russia, China and Germany, The Wall Street Journal reported. Then, Kerry and Zarif met alone.
The recent election of Iranian President Hassan Rouhani, widely considered more moderate than his predecessor, seems to have opened the possibility of a thaw in U.S.-Iranian relations, which had been frozen since Iran's 1979 revolution and the storming of the U.S. Embassy in Tehran, in which 52 embassy workers were held captive for 444 days.
Rouhani called Thursday for an end to nuclear weapons, saying disarmament "remains our highest priority."
"As long as nuclear weapons exist, the risk of their use, threat of use and proliferation persist," Rouhani told the U.N. General Assembly on behalf of the Non-Aligned Movement. "The only absolute guarantee is their total elimination."
During his speech before the U.N. General Assembly Tuesday, Obama said curbing Iran's pursuit of nuclear weapons and solving the Israeli-Palestinian conflict would be his highest foreign policy priorities for the remainder of his term.