It quoted Peres as saying that economic sanctions aimed at forcing Iran to abandon what Israel and the West say is a nuclear arms programme are starting to take effect.
“The sanctions are beginning to show some results,” he said.
“I think all of us agree that we should start with the non-military options while keeping all options on the table. If we can conclude it in a diplomatic way, then it’s much better.”
Peres’s office said that Israeli armed forces head Benny Gantz sat in on the meeting.
Dempsey arrived in the Jewish state on Sunday in conjunction with a massive US-Israeli missile defence drill, described by officials on both sides as the largest joint military exercise ever between the two allies.
“I know we’re having a joint exercise at the moment which is important,” Peres was quoted as telling Dempsey. “I want to thank you for coming and for your personal commitment to Israel’s security.”
Prime Minister Benjamin Netanyahu says that time is running out for the diplomatic option and the moment for military force is fast approaching.
He has urged US President Barack Obama to define clear “red lines” for Tehran, along with the consequences of crossing them.
Obama says that the use of force remains an option, but that there is still time for diplomacy to work.
“I think it is our commitment to remaining strong militarily together that provides the foundation for the other instrument of power to be applied,” Peres’s office quoted Dempsey as telling him.
Gantz earlier had his own meeting with Dempsey at military headquarters in Tel Aviv, discussing what an Israeli military statement called “aspects of military cooperation and shared security challenges.”
Meanwhile, Israeli Defence Minister Ehud Barak flew to Britain on Monday for talks with senior defence officials and Foreign Secretary William Hague, Barak’s office said in a statement.
It did not elaborate on the reason for the trip, but talks were likely to centre on Iran’s nuclear ambitions and instability in Syria and elsewhere in the Middle East.
Last month Britain’s Daily Mail newspaper said that the head of Britain’s foreign intelligence agency MI6 had visited Israel to warn Netanyahu against military action on Iran.
Sir John Sawers was also reported to have met Barak and a number of security and diplomatic officials.
On Sunday Barak met Dempsey and a statement from his office said they discussed the exercise, known as “Austere Challenge 12” and talked about “all current regional matters.”
