Annan calls for direct U.S.-Iran nuclear talks
He made the suggestion in an interview on The Newshour with Jim Lehrer on U.S. public television stations.
Annan has long been pushing for a diplomatic solution to Iran's nuclear activities.
Britain, France and Germany, with U.S. backing, on Wednesday circulated a draft UN Security Council resolution demanding that Iran suspend its nuclear activities.
"If everybody -- all of the stakeholders and the key players -- were around the table, I think it would be possible to work out a package that would satisfy the concerns of everybody," Annan said when asked whether it was time for the United States to get involved in direct talks.
In the earlier EU-Iran talks, Annan said he had the impression the Iranians had been hesitant to fully engage because whatever they discussed with the Europeans had to be checked with the United States.
"When you are in that sort of a mood, given their own culture, you probably don't put everything on the table," Annan said.
He said the Iranians could soon find themselves in a difficult situation after assuring the world they were not seeking nuclear weapons.
Should they be offered a diplomatic package allowing them to pursue nuclear energy for peaceful ends "and they resist that, how do they explain it to the world?" he asked.
Fischer urges U.S. dialogue with Iran
Former German foreign minister Joschka Fischer on Thursday urged the United States to adopt a carrot and stick approach to the nuclear crisis with Iran and warned that time was running out, AFP reported.
Speaking at the American Society on International Law, Fischer, who was foreign minister from October 1998 to November, said the carrot would be offering Tehran security guarantees and full diplomatic relations if it ends its nuclear activities.
The stick would be a serious threat to isolate the country economically and technologically if it went ahead with its nuclear program.
"It's not going to be easy to sell (this) to a national audience, neither in the United States nor in Europe, but if you know the grim alternatives I think this should be the offer," Fischer said, referring to possible military strikes against Iran.
"We are running short of time and without decided leadership on behalf of the United States I don't believe that this will work," he added.