Letta will ask Kerry for an explanation over recent reports that the US National Security Agency also spied on Italian international communications, Italian media reported.
Reports over the snooping have already angered French and Mexican officials and French Foreign Minister Laurent Fabius told Kerry in Paris at a meeting on Tuesday that it was "unacceptable".
Kerry landed in Rome late on Tuesday from London where he attended a meeting of the Friends of Syria group of 11 countries that agreed with Syrian opposition leaders that President Bashar al-Assad should play no future role in government.
Netanyahu, who is also visiting Rome, said after meeting Letta on Tuesday that it would be "tragic" if Iran succeeded in avoiding sanctions and proceeding with its nuclear programme.
"We must ensure that Iran will not have nuclear weapons capabilities and we can achieve this peacefully," he said, calling for pressure on Iran to be kept up despite the new president in place.
Last week, Iranian negotiators met in Geneva with representatives of six world powers. During the talks, Iran presented a new proposal to the West aimed at ending the nuclear stand-off.
"Iran says it wants a deal in which it will have civilian nuclear energy, but this is not the real issue," Netanyahu said on Tuesday, adding: "Many nations in Europe, North America, and Asia have nuclear energy without centrifuges or plutonium."
Netanyahu's office had also said he would meet with Pope Francis this week but officials later said this would not happen without explaining.
The meeting would have been the first between Netanyahu and Francis, who has been invited to the Holy Land by Palestinian leader Mahmud Abbas.