He is gauging global readiness to guarantee Iran's interests if it decides to remain in the nuclear pact a week after US President Donald Trump announced that the US was walking away from the JCPOA.
It termed the sanctions as illegal and warned that if talks to rescue the accord fail, it would ramp up its nuclear program to a level more advanced than before.
"The speed of the process is and has to be fast", Mogherini told a late night press conference.
Following a meeting with Mohammad Javad Zarif, Iran's Foreign Minister, Federica Mogherini, EU external affairs chief, said the EU had agreed to work on several areas to keep the deal in place.
"It won't be easy, that's clear to all of us".
The group likened the state of the deal to a "relative in intensive care", according to Mogherini.
Mogherini said European Union experts were aiming to come up with concrete proposals in the coming weeks on nine key issues including ensuring Iran could sell its oil and gas products and have access to worldwide finance.
Speaking as he left the meeting, Zarif said: "We are on the right track ... a lot will depend on what we can do in next few weeks".
"We are working with our European Union colleagues and directly both with the USA and with the European Union to try and both protect our businesses as well as encourage the U.S.to allow us to continue economic ties because we think that's important", she said.
Zarif said little to reporters Tuesday but suggested he wanted to discuss the deaths of dozens of Palestinians in Gaza as well as the nuclear deal, which U.S. President Donald Trump withdrew from last week.
The EU wants to ensure exports to Iran, which have exploded since the deal was signed in 2013, can continue.
Mogherini acknowledged the enormous challenge of finding a way around United States sanctions punishing businesses trading with Iran, which apply all around the world.
French exports to Iran doubled a year ago to €1.5bn, while German exports rose by €400m to €3bn.
While Mr. Trump's national security adviser, John R. Bolton, has said that the American intention is to force Iran into new, broader negotiations, European officials said they had heard no American strategy for doing that.
"We know it's a hard task but we are determined to do it and we have started to work to put in place measures that help ensure this happens", she told reporters.
"As long as Iran respects the provisions of the deal, the EU will also respect it", said Donald Tusk, president of the European Council and chairman of the leaders' gathering in the Bulgarian capital Sofia.