"I invite member states which are in a position to do so to make the necessary funding available as soon as possible, in order to ensure smooth continuation of our services," Yukiya Amano told an extraordinary meeting of the International Atomic Energy Agency's (IAEA) board of governors.
Amano said the Vienna-based watchdog's inspections workload had been "greatly increased", and that many staff "will give up their Christmas and New Year holidays this year", according to the text of his remarks.
Last month in Vienna, Iran and six world powers for the second time missed a deadline to strike an historic accord limiting the scope of Tehran's nuclear programme and easing fears that it might develop nuclear weapons.
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Iran and the five permanent members of the UN Security Council plus Germany gave themselves until June 30, 2015 to seal the deal, which would see painful sanctions on Iran lifted.
During this time an interim accord concluded in November 2013 will remain in force, under which Iran ceased certain nuclear activities and submitted to beefed-up IAEA oversight in return for around $700 million in assets being unfrozen a month.
Certain countries have questioned the utility of some additional inspections, since the IAEA already kept close tabs on Iran's facilities before the 2013 deal, devoting more resources to its work on Iran than on any other country except Japan.
It remains unclear when and where the next round of talks between Iran and the so-called P5+1 powers will take place, with some reports saying it may happen later this month, possibly in Oman.
Iranian Foreign Minister Mohammad Javad Zarif said Tuesday that neither a date nor location have been determined, while Kazakhstan's foreign minister said in Washington that his country was willing to host the talks.