The "substantive" round of talks on Iranian nuclear issues touched upon some controversial problems, EU foreign policy chief Catherine Ashton and Iranian Foreign Minister Javad Zarif said on Wednesday in a joint statement after a two-day meeting in Vienna.

Ashton and Zarif said the "useful" talks covered core issues surrounding the Iranian nuclear issue, including enrichment, heavy water reactor, civilian cooperation and possible relief of sanctions on Iran.

Western nations are asking Iran to significantly scale back its nuclear program to ensure the peaceful nature of Tehran's nuclear plan. They are suspicious of plutonium enrichment at the Arak heavy water reactor.

Meanwhile, Iran wants the West to relieve sanctions imposed on the country.

A senior US official involved in the talks told reporters after the meeting that US and Iran understood each other better than before through the talks.

"We understand each other's stand," the official said, adding that US could not accept a heavy water reactor in Iran.

Iran and the six powers to the meeting, the United States, China, Russia, Britain, France and Germany, agreed that the next round of talks would reconvene on May 7 in Vienna, which would continue to discuss tough issues.

The three-day talks ended up earlier than planned to honor the Persian Nowruz holidays.

Iran and the six major states struck a 6-month interim deal in Geneva, according to which Iran would suspend some controversial nuclear activities starting on Jan. 20, while western states would lift some sanctions imposed on Iran.