The fate of the reactor in central Iran was one of the toughest sticking points in the long nuclear negotiations that led to an agreement in July.
Removing the core of the heavy water reactor to produce less plutonium is a crucial step before relief from economic sanctions agreed under the deal can start.
Under the terms of deal, Iran accepted the Arak heavy water reactor to be reconfigured so it cannot yield fissile plutonium usable in a nuclear bomb.
China, United States, France, Britain, Russia and Germany have agreed to participate in the redesign and the construction of the modernised reactor.
The Islamic Republic has said that the 40-megawatt, heavy-water plant is aimed at producing isotopes for cancer and other medical treatments, and has denied that any of its nuclear activity is geared at developing weapons.
The removal of core of Arak reactor will be one of the final steps that Iran must take for implementation of the nuclear deal, known as Joint Comprehensive Plan of Action (JCPOA).
Behrouz Kamalvandi, the spokesperson for Iran's atomic energy agency, said in an interview the Iranian Etemad newspaper published on Monday that "Iran has met its commitments under the July nuclear agreement earlier than expected".
"Implementation of JCPOA will finish in the next 7 days," he added.
Iranian President Hassan Rouhani said in a speech broadcast live on state television on Monday: "We are hopeful that the sanctions against Iran would be lifted in the next few days."