"We must join hands and free our economic territory which was unjustly occupied by the countries of the P5+1 (Britain, China, France, Russia, the United States and Germany) and the UN Security Council ... through use of diplomatic and political tools," Rouhani said in a televised speech.
The P5+1 group is trying to negotiate a deal with Tehran aimed at preventing Iran from developing nuclear weapons, in exchange for an easing of punishing economic sanctions.
Iranian hardliners have opposed any deal curbing nuclear activities that Tehran says are for peaceful energy purposes.
The UN Security Council adopted six resolutions, four of which imposed sanctions, against Iran's nuclear and missile programmes between 2006 and 2010.
Since 2012, the United States and the European Union have also applied a series of unilateral sanctions that specifically target the energy and banking sectors.
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Iranian oil exports have fallen from more than 2.2 million barrels per day (bpd) in 2011 to about 1.3 million bpd, and Iran is banned from the SWIFT global banking network.
"The enemies keep us from selling our oil," Rouhani said in the speech to mark the 33rd anniversary of the liberation of the Iranian city of Khorramshahr, a symbolic victory in the Iran-Iraq war of 1980-1988.
The banking industry is also under a form of occupation because "we cannot send or receive money" overseas, he said.
"It is as if blood was prevented from flowing in (our) veins," Rouhani added.
In early April Tehran and world powers concluded a framework agreement aiming to pave the way for a final nuclear agreement by June 30.
Political and technical experts from both sides held talks on drafting the text in Vienna on Friday with negotiations due to resume on Tuesday in the Austrian capital.