Ashton will represent six powers - the United States, Russia, China, France, Britain and Germany - in dealings with Iran, and her offer of talks came after weeks of consultations with them.
It follows the expansion of sanctions by Europe and the United States to exert economic pressure and force Tehran to hold back on its nuclear program, which they fear aims to produce atomic weapons. Iran says it is enriching uranium for peaceful purposes only.
In a letter last month, Iran's chief nuclear negotiator, Saeed Jalili, proposed that negotiations with global powers should resume after more than a year's standstill, and said Tehran would have "new initiatives" to bring to the table.
"Today I have replied to Dr Jalili's letter of February 14," Ashton said in a statement. "I have offered to resume talks with Iran on the nuclear issue," she said.
Ashton's letter proposed an initial round of talks to focus on building confidence by developing concrete steps for the future.
"Our overall goal remains a comprehensive negotiated, long-term solution which restores international confidence in the exclusively peaceful nature of Iran's nuclear program, while respecting Iran's right to the peaceful use of nuclear energy," she said in her reply to Jalili.
President Barack Obama said an announcement of six-power talks with Iran offered a diplomatic chance to defuse a crisis over its nuclear program and quiet the "drums of war."
With Israel speaking increasingly loudly of resorting to military action, the talks could provide some respite in a crisis that has driven up oil prices and threatened to suck the United States into its third major war in a decade.
Time and venue to be confirmed
Ashton said the time and venue for talks should now be decided but noted she wanted talks to resume as soon as possible.
"In practical terms," she wrote, "our deputies could get together in the near future in order to prepare for the first round of our resumed talks."
In another possible step towards greater cooperation, Iran said yesterday it would let UN nuclear investigators visit a military complex where they had been refused access, to check intelligence suggesting Tehran has pursued explosives research relevant to nuclear weapons.
Western states are likely to tread cautiously, mindful of past accusations that Iran's willingness to talk has been a tool to buy time and not a path to agreement.