Moscow said on Friday that a free trade pact is to be signed next week between Iran and the Eurasian Economic Union, which includes Kazakhstan, Belarus, Armenia, and Kyrgyzstan.
After an hour-long meeting at European Union headquarters, Zarif said he believed both side were "on the right track" to make sure that the interests of the deal's "remaining participants, particularly Iran, will be preserved and guaranteed". The deal's official name is the Joint Comprehensive Plan of Action or JCPOA.
Even the USA needs global partners, she cautioned, saying: "No country is big enough to face this world alone".
Mohammad Javad Zarif's tour starts two days after unprecedented Israeli strikes in Syria which a monitor said killed at least 11 Iranian fighters, triggering fears of a broader conflict between the two arch-enemies. Foreign firms that continue doing business in Iran will face USA penalties once the sanctions come into force.
The European Union insists the deal is working, pointing to repeated United Nations inspections verifying the Islamic republic's compliance with its side of the bargain.
France and Germany also intend to stick to the agreement.
European leaders are walking a fine line in trying to save the accord with Iran and to safeguard the investments of their companies.
This echoes statements from China, which has also said it wanted to continue normal business ties with Iran and is now financing multi billion dollar infrastructure and electricity projects in the country.
In his statement, Zarif accused Trump of "ignorance and folly" and said American foreign policy had "dragged the Middle East into chaos".
Maas, who was on his first trip to Moscow, said it's important to maintain a frank and constructive dialogue with Russian Federation despite differences.
Zarif will then travel to Brussels for talks with the European countries that are party to the JCPOA on the possibility of preserving the accord with Iran's interests at its heart. At the same time, the country would make preparations to restart its program of nuclear enrichment, he said.
On Sunday, US Secretary of State Mike Pompeo said Washington still wants to work with Europe to counter Iran's "malign behaviour" and was working hard to thrash out a more wide-ranging deal with its European partners.
Under the 2015 deal, Iran would reduce its ability to enrich uranium and allow inspections by an independent agency in return for the lifting of strict sanctions which were choking the country's stagnating economy.