Grossi's visit came at a time of heightened regional tensions and with his International Atomic Energy Agency (IAEA) criticising Iran for lack of cooperation on inspections and other outstanding issues.
"The present state is completely unsatisfactory for me. We are almost at an impasse and this needs to be changed," Grossi told reporters at the airport in Vienna, where the IAEA is based.
He said there was no "magic wand" to solve a "very, very complex set of issues", while he pressed the Islamic republic to "deliver very soon".
"But of course, for me and also I would say for the international community, there is a need to have some results sooner rather than later," he said.
- 'Tangible measures' -
Earlier on Tuesday, at a news conference in the Iranian city of Isfahan, Grossi said he had proposed to Iranian officials that they "focus on the very concrete, very practical and tangible measures that can be implemented in order to accelerate" cooperation.
Grossi held talks with senior Iranian officials including Atomic Energy Organization's head Mohammad Eslami and spoke at Iran's first International Conference on Nuclear Science and Technology held in Isfahan.
Grossi insisted on the need to "settle differences" on the nuclear issue while the Middle East was going through "difficult times", particularly the war between Israel and the Iran-backed Palestinian militant group Hamas in the Gaza Strip.
"Sometimes, political conditions pose obstacles to full-fledged cooperation" between Iran and the international community, Grossi told reporters.
Grossi said a March 2023 agreement with Iran was "still valid" but required more "substance".
The agreement was reached during Grossi's last visit to Iran and outlined basic cooperation measures including on safeguards and monitoring.
The IAEA chief said, however, that there had been a "slowdown" in the agreement's implementation, including Iran reducing the number of inspections and withdrawing the accreditation of a group of IAEA experts.
- 'Good basis' -
Iran suspended compliance with a landmark 2015 deal setting caps on nuclear activities after the United States unilaterally withdrew from the agreement in 2018 and reimposed sweeping sanctions.
"We have this legal right to reduce our commitments when the other parties do not adhere to their obligations," Eslami said during the joint news conference in Isfahan.
Tensions between Iran and the IAEA have repeatedly flared since the deal fell apart, and EU-mediated efforts have so far failed to bring Washington back on board and to get Tehran to again comply with the terms of the accord.
The agency has repeatedly criticised Iran for a lack of cooperation on issues including the expansion of its nuclear work, the barring of inspectors and deactivating the agency's monitoring devices at its nuclear facilities.
In a report presented at its last Board of Governors meeting in March, the IAEA said that Iran's estimated stockpile of enriched uranium had reached 27 times the limit set out in the 2015 accord.
Iran has always denied any ambition to develop nuclear weapons capability, insisting its activities are entirely peaceful.
At the news conference, Eslami said the talks with Grossi were "constructive" and agreed that the 2023 agreement was a "good basis for interactions" between Iran and the agency.
Eslami denounced "hostile actions against the nuclear programme of the Islamic republic", in particular blaming Israel, Tehran's sworn enemy.
In response, Grossi said relations between the IAEA and Iran were not influenced by "external parties".
The three-day nuclear conference is being held in Isfahan province, home to the Natanz uranium enrichment plant and where strikes attributed to Israel hit last month, triggering an expression of concern by Grossi.
The IAEA and Iranian officials reported "no damage" to nuclear sites in the province.
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