Israel offered aid to its former strategic ally Turkey and their presidents spoke by telephone on Sunday. It was not immediately clear if Turkish side rejected the Israeli offer for aid or Barak was speculating as Turkish side has not replied to Israel.
"At this difficult time Israel is willing to provide any aid required anywhere in Turkey and at any time," President Shimon Peres told his Turkish counterpart Abdullah Gül, according to a statement issued by Peres's office.
Relations between Israel and Turkey have been frayed since Israeli commandos killed nine Turks during a raid on an aid flotilla bound for the Israeli-blockaded Gaza Strip in 2010.
Tension rose last month when Turkey expelled the Israeli ambassador after Israel refused to apologise for the killings, saying its marines acted in self-defence in confrontations with pro-Palestinian activists on one of the vessels.
Peres's conversation with Gül was believed to be the first between the two leaders since the envoy was expelled.
Gül told Peres that Turkey was still assessing the damage from the earthquake and that he hoped Turkish rescue teams could handle the disaster, the Israeli statement said.
Israeli foreign Ministry spokesman Yigal Palmor said Israel was willing to provide "anything from food, medicine, medical staff and equipment to search-and-rescue teams". He said Israel was awaiting Ankara's reply.
Despite their fraught relations, Turkey sent fire-fighting planes in December last year to help Israel battle a brush fire that killed 41 people.
In southeast Turkey, emergency workers battled to rescue people trapped in buildings in the city of Van and surrounding districts near the border with Iran. A local official said many people were killed or injured and tents and rescue teams were needed urgently.
Prime Minister Recep Tayyip Erdoğan told reporters on Sunday night during his visit to Van that at least 138 people were killed and hundreds are missing or wounded. Officials say death toll will rise.
"I speak as a person, a Jew and an Israeli who remembers and is well aware of the depth of the historic relations between our two peoples," Peres told Gül, according to the statement. "From this place, I send condolences on behalf of all Israel to the families of those killed."
Although Peres's office is largely ceremonial, he is briefed regularly by Prime Minister Benjamin Netanyahu on diplomatic affairs.
"The Turks are not interested in our aid this time," Barak told Israel's Channel 2, the Jerusalem Post reported on Sunday.
Israel has sent search and rescue teams to Turkey in the past after earthquakes struck. In 1999, an Israeli military rescue team pulled a 10-year-old Israeli girl out of the rubble of a collapsed building in Cirarcik in northwest Turkey, where her family was on holiday. She had been trapped for nearly 100 hours.
The team spent a week in Turkey, rescuing 12 people and recovering 140 bodies. Israel als set up a field hospital in the region, where two large quakes that year killed more than 20,000 people, treating more than 1,000 victims.
The report said Barak recalled previous natural disasters after which Israel provided aid and said "apparently there is a new reality."