In January, world powers led by the United States and the European Union lifted most sanctions on Iran in return for curbs on its nuclear programme.
But some U.S. sanctions remain, and U.S. banks remain prohibited from doing business with Iran directly or indirectly because Washington still accuses Tehran of "supporting terrorism".
That has deterred European institutions, which fear they could face U.S. legal problems if they re-establish banking links.
Zarif used the visit of EU foreign policy chief Federica Mogherini, the first by a high-level EU delegation since the deal came into force in January, to make his point.
"Iran and the EU will put pressure on the United States to facilitate the cooperation of non-American banks with Iran," Zarif said at a news conference in Tehran with Mogherini who said in a tweet that she was leading a team of seven EU commissioners.
"It's essential that the other side, especially the United States, fulfil its commitments not on paper but in practice and removes the obstacles especially in banking sector," he said.
Zarif and Mogherini said in a joint statement after the news conference that the EU and Iran were agreed on the expansion of economic relations, and "encouraging banking cooperation."
The White House said on Friday that an agreement with Iran does not include giving it access to the global financial system.
Iranian central bank Governor Valiollah Seif met U.S. Treasury Secretary Jack Lew on Thursday in Washington and said they discussed Iran's expectations under the nuclear deal.
Lew told Seif that the United States would keep meeting "its sanctions-related commitments in good faith" as long as Iran continues to uphold its end of the bargain.