The Iranian and P5+1 officials worked hard to coordinate elements that could be part of the final agreement, Mann said on Friday.
The parties exchanged views on several issues and started working on a draft agreement, he said.
The new round of Iran-P5+1 talks is scheduled for July 2, Mann said.
The P5+1 is a group of countries which in 2006 joined the diplomatic efforts with Iran in regard to its nuclear program. The term refers to the five permanent members of the UN Security Council plus Germany, namely the United States, Russia, China, United Kingdom, France, and Germany.