In a statement on Monday, the Majlis set out requirements for a nuclear deal with the major powers as Foreign Minister Mohammad Javad Zarif and US Secretary of State John Kerry held four hours of nuclear talks in the Swiss city of Lausanne.
The parliamentarians asked the nuclear negotiators to take account of the requirements in the talks with the P5+1 (the five permanent members of the UN Security Council plus Germany) on a final deal to resolve the 12-year dispute over Tehran's nuclear program.
The statement said a final agreement must lead to the lifting of all sanctions at once, close Iran's nuclear dossier at the UN Security Council, uphold the nuclear rights under the Non-Proliferation Treaty and stipulate that the deal would be considered null and void if the other side violated its terms.
After the meeting with Kerry, which followed Sunday's talks between Iranian, US and EU delegations involving Deputy Foreign Ministers Abbas Araqchi and Majid Takht-Ravanchi, Atomic Energy Organization of Iran Director Ali Akbar Salehi, EU political director Helga Schmid, US Secretary of Energy Ernest Moniz and Under Secretary of State for Political Affairs Wendy Sherman, Zarif said, "Solutions are within reach, but we still have differing views on some points."
The foreign minister had said on Sunday it is possible to reach a nuclear deal if the negotiating parties have the required "political will".
"In my view, if the other side has political will like the Islamic Republic of Iran, it will not be difficult to arrive at solutions," the chief nuclear negotiator said.
Later in the day, Zarif left Lausanne for Brussels to attend a nuclear meeting with EU foreign policy chief Federica Mogherini and the foreign ministers of the European members of the P5+1, namely France, Germany and Britain. He will return to the Swiss city on Tuesday for more talks with the US and the EU.
After his separate meeting with Moniz on Monday, Salehi told reporters he is "very optimistic" about the future of the talks, Fars news agency reported.
Iran and its international negotiating partners are trying to work out the framework of a long-term settlement to the nuclear dispute until the end of this month with a view to sealing a final deal by the self-imposed June 30 deadline.
Crucial Weeks
Reuters quoted Mogherini as saying on Monday nuclear talks were entering a critical stage, saying all sides still needed to find "common ground" to end the long-running standoff.
She said, "We are entering a crucial time, a crucial two weeks where negotiations will have to find the common ground for a good deal."
British Foreign Secretary Philip Hammond said a nuclear agreement still needed work.
"We are closer than we were but we've still got a long way to go," he told reporters as he arrived for an EU foreign ministers' meeting in the Belgian capital.
"There are areas where we've made progress, areas where we have yet to make any progress, but I think the fact that we are all here talking shows the commitment on all sides to try to reach an agreement," he said.
German Foreign Minister Frank-Walter Steinmeier said he believed that "if we have the chance to bring this conflict to a result after years and decades and more than 10 years of negotiations, that we should grab the chance."