"We are working very, very hard and we have some very difficult issues but we believe we're making progress and we're going to continue to work because of that," Kerry told reporters.
His comments, a day after negotiators gave themselves until July 7 to agree a deal, followed a meeting in the Austrian capital with Iranian Foreign Minister Mohammad Javad Zarif.
Earlier Zarif said: "We have made progress and we will make progress and we will use every opportunity to make progress."
The aim is to finalise a framework accord agreed in April under which Iran will curb its nuclear activities -- making any drive to make nuclear weapons all but impossible -- in exchange for relief from painful sanctions.