Hassan Rouhani, a moderate Iranian presidential candidate and former top nuclear negotiator, was elected president earlier this year.
- NEW: Iran's foreign minister, U.N. chief have positive meeting in New York
- John Kerry praises Iranian president's comments on talks, nuclear program
- Yet the top U.S. diplomat adds: "Everything needs to be put to the test"
- Rouhani called his exchange of letters with President Obama "positive and constructive"
(CNN) -- U.S. Secretary of State John Kerry on Thursday characterized recent remarks by Iran's new president regarding the standoff over his nation's nuclear program as "very positive," though he cautioned against jumping to the conclusion that any breakthrough is imminent.
Kerry declined to answer a question -- which he fielded while leaving a stage at the State Department where he'd talked about Syria -- about whether Iranian President Hassan Rouhani would meet with U.S. President Barack Obama when both attend the U.N. General Assembly next week in New York.
America's top diplomat had good things to say about comments made by Rouhani, including in an interview with NBC News.
Yet he offered his compliment with a caveat: "Everything needs to be put to the test, and we'll see where we go."
Iranian Foreign Minister Javad Zarif had what he called a "constructive" meeting Thursday with U.N. Secretary-General Ban Ki-moon, according to the state-run Islamic Republic News Agency. Zarif referred to "satisfactory negotiations" on various issues, including Iran's nuclear program, the report stated.
Ban's office also issued a statement on the meeting, saying the two "discussed Iran's growing cooperation with the international community on a host of issues, including the nuclear file, as well the role Iran could play in promoting a political solution to the conflict in Syria."
This encounter took place place in New York ahead of the General Assembly. Asked Wednesday if Rouhani and Obama themselves could get together face-to-face when they are both there, White House spokesman Jay Carney said "there are currently no plans" for such a meeting though he also didn't rule it out.
And Carney did hint the United States is open to talks with Iran -- with whom it has feuded regarding Iran's nuclear program, a dispute that's led to harsh international sanctions and raised the specter of war in the region -- to "test" whether Tehran is sincere in its hope to improve its international standing.
"I think it's fair to say that (Obama) believes there is an opportunity for diplomacy when it comes to the issues that have presented challenges to the United States and our allies with regards to Iran," Carney said. "And we hope that the Iranian government takes advantage of this opportunity."
In an interview Wednesday with NBC's Ann Curry, Rouhani said, "We have never pursued or sought a nuclear bomb and we are not going to do so."
There's little dispute Supreme Leader Ayatollah Ali Khamenei is Iran's most powerful figure. Still, Rouhani said Thursday that he and his delegation will head to New York with the "full power and has complete authority" to make a deal with others on nuclear matters.
Both Obama and Rouhani have mentioned trading letters since the latter's election this summer, an exchange Iran's president called "positive and constructive."
"It could be subtle and tiny steps for a very important future," Rouhani told NBC, according to video on the network's website. "I believe the leaders in all countries could think in their national interests and that they should not be under the influence of (interest) groups."
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Even as it has resisted attempts by international regulators to assess its development, Iran has long insisted its nuclear program's aim is to produce power, not weapons. Last month, Rouhani said the United States and other nations "need to recognize that our activities are totally peaceful and legal."
If they do and there are "negotiations without threats," Rouhani added, then "the way for interaction is open."
The 64-year-old cleric, who is considered moderate, won the June elections with reformist backing after a campaign in which he stressed "hope and prudence."
A former nuclear negotiator himself, he vowed to reduce the high tension between Iran and the outside world.
Rouhani has military experience as well, having once commanded Iranian air defenses and led three war and defense councils. He was national security adviser for 13 years before his presidential predecessor, Mahmoud Ahmadinejad, took office in 2005.
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CNN's Greg Botelho contributed to this report.
