President Hassan Rouhani said Wednesday he expects sanctions on Iran to be lifted by mid-January after the UN nuclear watchdog closed its probe into Iran's past efforts to develop nuclear weapons.

Iran and leading world powers reached a landmark agreement in July under which punishing economic sanctions will be rolled back in exchange for Iran curtailing its nuclear programme.

The end of the International Atomic Energy Agency (IAEA) investigation into "possible military dimensions" to the programme was a condition for the July deal to go forward.

Rouhani said "the final steps that we must take will be completed in the next two weeks and the sanctions will be lifted during the (Iranian calendar) month of Dey," which runs from December 22 to January 21.

"The chains of sanctions will be removed from the feet of the Iranian economy and the way will be opened to greater cooperation with the world," he said.

"We invite all economic actors in the country, all Iranians living abroad, all foreign companies that want to cooperate with Iran to profit from this opportunity to come to our country, which is the most secure in the region."

Iran has always denied pursuing an atomic weapon.

Under the deal, Iran pledged to slash the number of centrifuges -- which enrich uranium -- from around 19,000 to 6,104, of which 5,060 will still enrich.

It also has to change the design of a new nuclear reactor being built at Arak and shrink its stock of low-enriched uranium, shipping it to Russia.