The German government says Chancellor Angela Merkel and French President Emmanuel Macron have discussed the situation in a joint telephone call with Russian President Vladimir Putin.
Merkel's office said in a statement on Tuesday that the three leaders "underlined the need to persuade Iran to remain in the nuclear agreement, which they agreed to maintain", AP reported.
Iran announced the decision to stop parts of its obligations under the 2015 nuclear deal in early May, a year after the United States pulled out of the accord and reinstated the lifted sanctions on Tehran, according to Financial Tribune.
It also declared that it would further ease its commitment if the remaining signatories fail to safeguard Iran's oil and banking interests within 60 days.
The decision was made amid intensified economic and military pressures by Washington and other parties' failure to uphold Iran's rights under the agreement, known as the Joint Comprehensive Plan of Action.
The heightened tensions have raised concerns about the future of the deal, prompting the signatories to find ways of convincing Iran to refrain from suspending its commitments.
The Russian Foreign Ministry also on Tuesday called for a session of the JCPOA Joint Commission "so that the countries’ participants in the agreements jointly determine the ways for normalizing the situation [to guarantee] that the JCPOA stays".
"The necessity to convene a session of the JCPOA Joint Commission is getting increasingly evident," it said, hoping that "it will be possible to avert further escalation", TASS news agency reported.
It also urged European parties to complete their steps to address Iran's concerns.
"A lot depends on our European colleagues and their capability to duly react to Iran’s concerns, creating conditions for maintaining trade-economic ties with Iran for the interested European companies," the ministry said.
The EU has introduced a payment channel known as INSTEX (Instrument in Support of Trade Exchanges) through which Iran can conduct trade through a non-dollar system to bypass American sanctions.
It was registered after a long delay by France, Germany and Britain in late January, but has not been activated yet although Iran has set up a corresponding entity.
The financial vehicle aims to facilitate trade between Iran and EU in the first phase before expanding to cover major transactions like Iran’s oil exports and third parties.