“Our friendship is solid,” Mr Gul said at a press briefing this week with his counterpart Silvan Shalom during the most senior visit by a Turkish official to Israel since the Justice and Development Party, a movement with Islamist roots, came to power in Ankara in 2002.

Tensions had escalated last May, when Prime Minister Recep Tayyip Erdogan condemned as “state terror” a deadly Israeli operation in the Rafah region of southern Gaza and Ankara temporarily recalled its ambassador.

The move marked an unprecedented chill in relations, which had been close since 1996 when, to the anger of Arab nations and Iran, the two countries hammered out a military cooperation accord, followed by a sharp increase in trade and cultural exchanges.

“We agreed to intensify our collaboration to bring bilateral ties to new highs,” Mr Shalom said, hailing Israel’s “deep friendship and intimate dialogue” with Turkey.

Mr Gul underlined his country was eager to do all it could to help revive the Middle East peace process and said that Syria too was keen to participate.

“There is a new climate in the region… This opportunity should not be missed,” he said. “I believe they (the Syrians) wish to seek a lasting peace in the region.”

During talks with Prime Minister Ariel Sharon, Mr Gul reiterated his belief the Syrians were “sincere” in their desire for peace and stressed Turkey’s readiness to mediate in any talks, a senior source in the premier’s office said.

“Gul came with the clear intention of trying to be a mediator between Syria and Israel. He got the feeling that (Syrian President) Bashar al-Assad is sincere,” he said, while stressing Israel would need to see some kind of gesture before opening talks.

Turkey, a strictly secular non-Arab Muslim nation, believes it can help with peace initiatives across the region, drawing on its close ties with Israel and the Palestinians, and the remarkable improvement in its relations with Syria, a former foe.

Until now, however, the idea appears to have so far attracted little enthusiasm from Israel.

“Sincerity is a very good thing but we would like it to be shown in a gesture, like the expulsion of the terrorist headquarters which operate out of Damascus,” the source said.

“Once we see positive sincere steps — not just a gesture to ward off American pressure — we would be very willing to meet,” he said, saying Sharon asked Mr Gul to pass on the message to Damascus.

Similar comments were made by Mr Shalom, who welcomed Turkey’s mediation offer.

“We need to see an effort by Syria and Arabs to try to put an end to terrorism and incitement that is coming towards Israel from their countries.

“Turkey can also use its influence on the Palestinian Authority… to help them realise that the only way towards progress is to put an end to terrorism and violence,” he said.

Damascus would send “a very positive signal” to Israel if it also moves on humanitarian issues such as the long-sought return of the remains of Israeli spy Eli Cohen, executed in Syria four decades ago, Shalom said.

Mr Gul’s trip to Israel came hot on the heels of a high-profile visit by Turkish Prime Minister Erdogan to Damascus in December.

His talks with Israeli leaders are expected to pave the way for a visit to the Jewish state by Mr Erdogan later in the year.

Mr Gul will meet with Palestinian leaders on Wednesday, including PLO chief Mahmud Abbas, the frontrunner in the January 9 Palestinian presidential election.