Six world powers and Iran negotiated past a March 31 deadline into the wee hours of Wednesday, struggling to conclude an outline accord on Tehran's nuclear program in the face of a U.S. threat to abandon the talks.

With Iran asserting its "nuclear rights," the talks in the Swiss city of Lausanne entered a seventh day, bogged down this time on the issues of nuclear research, the lifting of U.N. sanctions and their restoration if Iran breached the agreement.

Officials cautioned that any accord would be fragile and incomplete, but the U.S. State Department gave the go-ahead for talks to go past a self-imposed midnight deadline.