Geneva, Switzerland (CNN) -- Iran and international powers finished two days of talks centered on Iran's controversial nuclear program Tuesday and both sides agreed to meet again in Turkey next month.
But Iran insists that its nuclear aspirations are not negotiable.
"We are ready to address and to seek common ground also on other issues of mutual interest. We and Iran agreed to a continuation of these talks in late January in Istanbul, where we plan to discuss practical ideas and ways of cooperating towards a resolution of our core concerns about the nuclear issue," said Catherine Ashton, the European Union's foreign policy chief.
Saeed Jalili, Iran's top nuclear official, told reporters that the "only outcome" from the latest talks was an agreement to meet in the Turkish city for discussions that would focus on "cooperation to find common ground."
"Any effort to deny nations their inalienable rights is not acceptable," he said.
The meetings in Switzerland were between Iran and what is known as the P5 plus 1, the five permanent members of the U.N. Security Council -- the United States, China, France, Russia and the United Kingdom -- plus Germany. The group has been meeting intermittently, with the last previous round of talks coming over a year ago.
The United States, other Western countries and Israel fear that Iran wants to develop nuclear weapons, an allegation Tehran has always denied. Iran already faces stiff sanctions from the international community because it has continued to enrich uranium.
A recent WikiLeaks disclosure revealed that concern over the program extends to the Arab world. Saudi Arabia's King Abdullah urged the United States to attack Iran to halt its nuclear program, warning that if Tehran were to go nuclear, other countries in the region would too.
In a written statement, Ashton said there were "nearly two days of detailed substantive talks" that focused "on the Iranian nuclear programme and the need for Iran to comply with its international obligations.
"Countries I represent are united in seeking a resolution of the international community's concerns regarding Iran's nuclear programme -- which is the central purpose of these talks. We recognise Iran's rights, but insist that it fulfils its obligations," the statement said.
A diplomatic source familiar with the talks said Iran's nuclear program was the main issue on the table during the talks.
Iran has previously said it did not want the meeting to focus on that topic, and it raised some of its own concerns, including attacks on two Iranian scientists in Tehran last week that left one dead and one injured.
Iran blamed Israel, the spy agencies of the United States and the United Kingdom for the attacks.
In his appearance before reporters, Jalili reiterated Iran's point that it has the right to develop nuclear power for peaceful purposes and that there can be no bargaining over that activity.
He expressed concern over the existence of nuclear arsenals and the existence of nuclear warheads harbored by other countries. Also, he singled out the regime's worries over Israel's arsenal and said that the international community is concerned about U.S. disarmament.
"Who is giving nuclear weapons to the Zionist regime?" Jalili asked. Israel has never confirmed that it has nuclear weaponry.
Jalili raised the issue of the attacks on the nuclear scientists, saying that they stem from the desire of other powers in the world to monopolize science.
As for talks, Jalili said discussions in which other parties "will use pressure to push their agenda" will fail.
He said Iran has capacities that it can bring to the table and "we do believe that we can sit down and talk about common concerns" -- such as security and economics.
Jalili was asked what would happen if talks fail and if Iran is worried that it faces isolation. He said sanctions aren't working and the community is prospering.
He said he expressed an interest in a joint news conference with Ashton, but she apparently had some prior engagement and couldn't attend.
The Turkish foreign ministry said Ashton told Turkish officials that the talks "were taking place in a positive atmosphere" and Turkey's efforts were "appreciated."
"Our minister stated that they were glad that the talks started in a constructive framework, that Turkey would continue to contribute to global and regional peace and that we would be glad to host the parties in our country."
Asked about the WikiLeaks revelations concerning regional fears over its nuclear program, Jailili said "our ties are strong with our neighbors and we have the best of relations with them."
He added, "To those parties who have engaged in mischief and by engaging in mischief, they are trying to tarnish the long-standing, historical and friendly relations between the Islamic nation of Iran and its neighbors, let me tell them they will not succeed."
CNN Senior International Correspondent Matthew Chance contributed to this report.