Officials from Western nations involved in the talks acknowledged huge differences between the two sides but insisted the diplomatic track had not been derailed. But the lack of progress in Moscow is sure to be seen by critics as a sign that talks are ineffective at persuading Tehran to curb uranium enrichment, a process that can make both reactor fuel and the core of nuclear warheads.
Strong comments by Foreign Minister Laurent Fabius of France, one of the countries at the table in Moscow, reflected Western frustration. He spoke of "the large gap between the two sides" and warned that "sanctions will continue to be toughened" to pressure Tehran into a nuclear compromise.
Iran says it is not interested in nuclear weapons. But Israel says Iran is stretching out the talks to move closer to the ability to make them, and it has threatened to attack the Iranians as a last resort. Israel may argue that the negotiations are turning into "talks about talks" - something the United States and its allies have vowed they will not tolerate.
Ahead of the inconclusive last round of talks in Baghdad on May 23, Israeli Prime Minister Benjamin Netanyahu accused Tehran of playing a "chess game" with the international community, declaring he saw "no evidence whatsoever that Iran is serious about ending its nuclear program."
Netanyahu did not present any ultimatums then, but Israeli officials have repeatedly said time is running out to avoid military action as a last resort to prevent Tehran from developing nuclear arms. It is a scenario with potential to draw the United States into a war between the Jewish state and Iran.
Ashton, who convened the talks between Iran and the six powers - the United States, Russia, China, Britain, France, and Germany - defended the decision to kick contacts down to a lower level.
She said it was "the right way to go forward" and suggested Iran's actions would determine if negotiations between top officials resumed.
"We expect Iran to decide whether it is willing to make diplomacy work, to focus on reaching agreement on concrete confidence-building steps, and to address the concerns of the international community," Ashton said in a statement.