"I sincerely hope that through the (Iran-G5+1) negotiations there will be very meaningful progress," the UN chief said on Thursday.
Ban urged Iran and the Group 5+1 to show flexibility, reiterating that issues related to the Iranian nuclear energy program should be settled through completely peaceful means as soon as possible.
Representatives of Iran and the Group 5+1 (the US, Britain, France, Russia and China plus Germany) started a fresh round of talks in Almaty's Rixos Hotel, Kazakhstan, on Friday.
Secretary of Iran's Supreme National Security Council (SNSC) Saeed Jalili heads the Islamic Republic's negotiating delegation. The G5+1's representatives are led by EU foreign policy chief Catherine Ashton.
On Thursday, Iran's deputy chief negotiator Ali Baqeri said that the Islamic Republic would enter the new round of talks with the G5+1 with clear, groundbreaking proposals.
The last round of the talks between Tehran and the six world powers was held in Almaty on February 26-27.
Also, experts from Iran and the G5+1 reviewed the two sides' proposals in a meeting in Istanbul from March 17 to 18. The two sides' experts outlined topics of the talks between the chief negotiators of Iran and the G5+1.