During the phone talks, President Rouhani stressed that mutual respect should underlie the talks and any final nuclear deal between Tehran and the six world powers, and reiterating that Iran sees removal of all sanctions as an indispensable part of any agreement.
During his phone conversation with British Prime Minister David Cameron, President Rouhani cautioned the world powers not to miss the present chance for striking a deal with Iran, and described "full annulment of sanctions as the most essential component of the negotiations for moving towards a final settlement" of the differences and attainment of a final deal over Iran's nuclear issue.
He also called for a replacement of confrontational approaches with a policy based on future cooperation through confidence-building.
The phone talk came as a fresh round of nuclear negotiations started Lausanne on Thursday.
The Iranian foreign minister's deputies, Seyed Abbas Araqchi and Majid Takht Ravanchi, had their first round of talks with their US counterpart Wendy Sherman this morning.
Later, Iranian Foreign Minister Mohammad Javad Zarif also held a meeting with his US counterpart John Kerry in the presence of their deputies, Head of the Atomic Energy Organization of Iran (AEOI) Ali akbar Salehi, US Energy Secretary Ernest Moniz, EU foreign policy chief Federica Mogherini and her deputy Helga Schmid in Lausanne.
The French foreign minister - whose country has reportedly taken the toughest stance against Iran in the current round of the nuclear negotiations - is also due to join the talks on Saturday.
The last round of talks between the Iranian and US nuclear negotiators ended in Lausanne last Friday afternoon in the presence of Zarif, Kerry, their deputies, Salehi, Moniz, and Schmid. The Iranian negotiators returned to Tehran on Saturday to participate in ceremonies celebrating the Iranian new year (which started on March 21).
Zarif said on Saturday that Tehran and the 5+1 group of powers had found technical and political solutions to their differences.
"Proper technical and political solutions have been found for the issues which couldn't be solved in the past," Zarif wrote on his facebook page.
"We were ready for negotiations, but the other sides needed more time for coordination," he added.
"We have decided to return to Geneva on Wednesday to continue the talks, and God willingly, finalize the details of the solutions," Zarif said.
After the last round of talks with powers on Friday, Araqchi said that the US and European countries needed more consultations and arrangements with their governments to continue talks with Iran.
Talks between Iran and Group 5+1 (the US, Russia, China, Britain and France plus Germany) were very serious and extensive, he said, adding that nuclear teams at this juncture are in need of more negotiations and coordination.
Owing to the same reason, foreign ministers of the European states and the US met in Berlin on Saturday to get ready for the new round of the negotiations today.
Iran and the G5+1 are negotiating to narrow their differences over Tehran's nuclear energy program ahead of a July 1 deadline.
Zarif underlined on Friday that the ball was in Washington's court to make a choice between a final deal or ineffective pressures against Tehran.
"Iranians have already made their choice: Engage with dignity," Zarif wrote in her tweeter page.
"It's high time for the US and its allies to chose: pressure or agreement," he added.
Earlier this month, Salehi announced that Tehran and Washington had overcome their differences on technical issues with regard to Iran's nuclear program in most of the cases, adding that both sides were trying to resolve the remaining technical problems.
"We have agreed on 90 percent of technical issues," Salehi said after his second meeting with Moniz in Lausanne, Switzerland, in mid March.
"There has only remained one very important point of difference that we will try to resolve in the evening talks," he added.
Both Iran and the G5+1 negotiators have underlined that cutting a final deal before the July 10 deadline is possible.
In relevant remarks earlier this month, Zarif said there was still a good chance for the success of the nuclear talks between Tehran and the world powers, but meantime underlined that failure of the negotiations would never mean the end of world to Iran.
"There is still an over 50-percent chance for the attainment of an agreement and I feel that both sides believe that success and attainment of an agreement will be much better and useful than failure in the negotiations; yet, failure in reaching an understanding will not be the end of the world but both sides have spent their time and political prestige in the success of these talks," Zarif said in an interview.
He stressed that the chances for the failure of the talks would be alive as long as agreement was not attained on all issues and details, and said, "As it was said in the Geneva agreement (November 2013), as long as an agreement is not made on all issues, nothing has been agreed on."
Asked about the removal of the sanctions against Iran, Zarif said, "Removal of the UN Security Council sanctions aren’t complicated and merely depends on the political will (of the other side)."