The result was 10 hours of intensive talks, in which all sides were determined to ensure a second round to discuss real details, now set for May 23 in Baghdad.
Speaking after the talks, Ms. Ashton said they were "constructive and useful," and the start of a "sustained process of serious dialogue."
One senior American official said the Iranians "brought ideas to the table," but that the US would continue its dual-track policy of pressure and diplomacy.
"Dialogue is not sufficient for any sanctions relief," the US official said. "One has to get to concrete actions that are significant."
Perhaps most important to the Iranians may have been the agreement that the Nuclear Nonproliferation Treaty (NPT) is the framework to ensure that Iran's nuclear programs are peaceful.
The NPT, Ashton said, will form "a key basis for what must be serious engagement, to ensure all the obligations under the NPT are met by Iran while fully respecting Iran's right to the peaceful use of nuclear energy."