Mogherini also told reporters on Tuesday during her trip to Wellington, New Zealand, that it's up to Europeans to decide who they want to trade with.
"We are doing our best to keep Iran in the deal, to keep Iran benefiting from the economic benefits that the agreement brings to the people of Iran because we believe this is in the security interests of not only our region, but also of the world. If there is one piece of international agreements on nuclear non-proliferation that is delivering, it has to be maintained," Mogherini was quoted by AP as saying.
The United States reimposed stiff economic sanctions on Iran on Monday, ratcheting up pressure on the Islamic Republic despite statements of deep dismay from European allies, three months after Donald Trump pulled the US out of the international accord limiting Iran's nuclear activities, Financial Tribune reported.
Iran accused the US of reneging on the nuclear agreement, signed by the previous American administration, and of causing recent Iranian economic unrest.
European allies said they "deeply regret" the US action.
A first set of reimposed US sanctions affects financial transactions that involve US dollars, Iran's automotive sector, the purchase of commercial planes and metals, including gold.
A second batch of US sanctions targeting Iran's oil sector and central bank are to be reimposed in early November.
Trump warned that those who don't wind down their economic ties to Iran "risk severe consequences".
European ministers said the Iran deal was crucial for Europe's and the world's security and the European Union issued a "blocking statute" on Monday to protect European businesses from the impact of the sanctions.
The mechanism, which took effect beginning at midnight Washington time (0400 GMT Tuesday), stops European companies from complying with the US sanctions unless they have authorization from the commission. National governments could impose "effective, proportionate and dissuasive penalties" on any of their companies that cave in.
The statute also blocks the effects of US court actions in Europe and allows European firms to recover damages arising from the sanctions from anyone who causes them.
Mogherini, speaking at a news conference alongside New Zealand Foreign Minister Winston Peters, said the EU and New Zealand saw the need to maintain the nuclear deal with Iran, notwithstanding the US withdrawal, and that she and Peters had discussed in detail how to keep open trade and financial channels with Iran.
"We are encouraging small and medium enterprises in particular to increase business with and in Iran as part of something (that) for us is a security priority," Mogherini said, explaining that trade is an integral part of the nuclear deal.
According to Independent, UK Foreign Secretary Jeremy Hunt signed a joint statement with other EU foreign ministers to ensure European companies doing business with Iran will be protected.
Trade between Iran and the EU "is a fundamental aspect of the Iranian right to have an economic advantage in exchange for what they have done so far, which is being compliant with all their nuclear-related commitments," Mogherini said.
Latest Eurostat data show trade between Iran and 28 member states of the European Union during the first half of 2018 amounted to more than €8.3 billion, registering a 12.8% decrease compared with last year’s corresponding period.
Iran exported €4.68 billion worth of commodities to the EU members during the period, indicating a 2.2% fall and imported €3.61 billion, down 23.7% year-on-year.
Germany's Economy Ministry said on Monday the country will continue to offer export and investment guarantees for companies doing business with Iran, adding that Berlin remained in dialogue with the US on exemptions for German companies from Iran sanctions.
“Export guarantees and investment guarantees from the Federal Ministry of Economics are still available to companies,” the ministry said.