The talks in Vienna came a day after Kerry and the foreign ministers of Britain, France and Germany failed to reach a breakthrough on uranium enrichment and other issues standing in the way of a deal that would curb Iran's nuclear program in exchange for the end of nuclear-related sanctions on Tehran.
Kerry and Iranian Foreign Minister Moahmmed Javad Zarif spoke for about two hours around midday Monday. They gathered again in the afternoon.
"I am glad that we can have some time to be able to catch up and pick up where we left off," Kerry told his Iranian counterpart as their first session got underway.
Asked after his second meeting about progress, Kerry told reporters: "We're working away."
After taking turns meeting with Zarif Sunday, Kerry and his European counterparts each described significant gaps between the two sides. Russia and China sent lower-level officials to Austria's capital for this week's gathering.
Six months ago, the six world powers and Tehran gave themselves until July 20 to conclude what is supposed to be a multi-decade agreement that sets clear limits on Iranian activity and locks in place an international monitoring regime designed to ensure that the Islamic Republic cannot develop nuclear weapons.
But the interim agreement also provides the option of an additional six-month window for hammering out a full accord, though officials have suggested a shorter extension may be agreed upon.
Kerry's second day of talks will continue his efforts to gauge "Iran's willingness to make the critical choices it needs to make," according to a senior State Department official.
The official didn't say how long Kerry's discussions with Zarif would run, but indicated a "potentially lengthy conversation" lay ahead. The official wasn't authorized to be quoted by name and demanded anonymity.
Zarif said Sunday no problems had been resolved "but I think we have made some important headway."
Iran says it needs to expand enrichment to make reactor fuel and insists it does not want atomic arms. But the U.S. and others fear Tehran could steer the activity toward manufacturing the core of nuclear missiles. Washington is leading the charge for deep Iranian enrichment cuts.
Germany's Frank-Walter Steinmeier and France's Laurent Fabius left Sunday, a few hours after they arrived. But Hague joined Kerry in staying on for another day.
The show of Western unity notwithstanding, Kerry's presence was most important. With the most significant disputes between Washington and Tehran, his visit gave him a chance to discuss them directly with Zarif.
Both face difficult internal pressures.
Iranian hardliners oppose almost any concession by moderate President Hassan Rouhani's government. In the U.S., White House officials have been wary of the prospect of another extension because it would be harder to hold off congressional sanctions against Iran if the negotiations drag on. Republicans and Democrats in Congress have threatened to scuttle any emerging agreement because it would allow Iran to maintain some enrichment capacity
Outside the negotiations, regional rivals of Iran, including Israel and Saudi Arabia, are extremely skeptical of any arrangement they feel would allow the Islamic republic to escape international pressure while moving closer to the nuclear club.
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