"I am under the impression the Turks do not want our help," Barak told Channel 2 News. "Right now (their answer) is negative but if they see they need more aid and don't have it, or if they rethink it, we have made the offer and remain prepared (to help)," he said.
A Turkish foreign ministry official said later that Turkey had received offers of help from dozens of countries after the magnitude 7.2 quake, and had so far declined assistance from all of them.
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 apologize for the killings, saying its marines acted in self-defense in confrontations with pro-Palestinian activists on one of the vessels.
Israeli Prime Minister Benjamin Netanyahu said he had told all branches of government to offer whatever help they could to the people of Turkey. "I think this is what neighbors should be doing with one another," he told reporters.
"At this difficult time Israel is willing to provide any aid required anywhere in Turkey and at any time," Peres told Gul, according to a statement issued by Peres's office.
Gul 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.
Despite their fraught relations, Turkey sent fire-fighting planes in December last year to help Israel battle a brush fire that killed 41 people.
Emergency workers battled to rescue people trapped in buildings in the Turkish town of Ercit 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.
Deputy Prime Minister Dan Meridor said Israel must "do what we can to rebuild ties with Turkey" which he described as a strong, stable state and Western ally in a turbulent region.
"Both countries, which can be and were once, anchors of stability in the Mideast, have a joint interest in co-operating and I hope this returns," Meridor told Channel 1 television.
Israel has sent rescue teams to Turkey in the past after earthquakes struck. In 1999, an Israeli military rescue team pulled a 10-year-old Israeli girl from 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 also 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.