Tajani arrived in Israel just as Prime Minister Benjamin Netanyahu returned from a trip to Italy.
Grossi's statements came after extended meetings with key officials in Iran over the weekend.
"Are we forbidden from defending ourselves? We are obviously permitted to do this," Prime Minister Benjamin Netanyahu told his cabinet in a televised speech Saturday night.
Iran is supposed to provide access to information, locations and people, suggesting a vast improvement after years of Iranian stonewalling.
Israel is also expected to ask Germany to designate the Iran Islamic Revolutionary Guard as a terror entity.
The Iranians are leveraging every opportunity to acquire strategic military capabilities and hardware that were previously out of their reach.
After a 2015 deal, Iran shipped all their enriched uranium to Moscow. Now, should the West worry about Russia?
Andrew Jenkinson claims in his new book that security faults were made public knowledge years ago but few attempts were made to rectify them.
Iran's arming of Russia crossed a red line and Tehran appears to believe it cannot go back - instead it's increasing its cooperation with Moscow.
Hayman also answered questions regarding the Iran nuclear deal, which was shelved in 2018 when Trump took office and has yet to be reinstated, despite efforts from both sides.