Ashton, who represents the P5+1 group -- the five UN Security Council permanent members Britain, China, France, Russia and the United States plus Germany -- during the talks with Iran made the announcement at the Palace of Nations, the headquarters of United Nations Office in Geneva, Xinhua reported.
"We have reached an agreement," Iranian Foreign Minister Mohammad Javad Zarif also announced on his Twitter.
No details of the agreement have been released as yet.
P5+1 group and Iran have reached a first-step agreement on Iran's nuke program.
The latest round of the Iran nuclear talks, which started Wednesday and were scheduled to conclude Friday, entered into the unscheduled fourth day Saturday.
The United States Secretary of State John Kerry and foreign ministers of the five other major countries arrived here to push for a breakthrough.
This was the third round of negotiations between Iran and the six countries in more than a month.
Western countries have long been accusing Iran of developing nuclear weapons under the cover of a civilian nuclear program, but Iran insists that its nuclear program is for peaceful purposes.
In response to the deal, White House has said Iran is committed to halting enrichment above five percent and neutralizing stockpile of nearly 20 percent Uranium.
Acknowledging challenges ahead in talks with Iran, US President Barack Obama said after the deal that the United States and Iran can chip away mistrust.