* Israel protests to Turkish diplomat
* Israeli PM hopes Turkey not moving towards extremism
* TV drama was "state-sponsored incitement", Israel says
(Adds Netanyahu comments)
By Joseph Nasr
JERUSALEM, Oct 15 (Reuters) - A Turkish television drama which depicts an Israeli soldier shooting dead a Palestinian baby has strained already tense relations between Israel and Turkey, its strategic Muslim ally.
Once-close ties between the Jewish state and Turkey, a secular state with a Muslim population, have deteriorated since Israel’s offensive earlier this year in the Palestinian Gaza Strip, ruled by the Islamist group Hamas.
Israel on Thursday summoned a Turkish diplomat to protest at "state-sponsored incitement" by state-owned TRT television’s "Separation" series, in which actors playing Israeli soldiers and Palestinians fight street battles in Jerusalem.
"The series, which has no connection to reality whatsoever, is not even suitable for an enemy country and certainly not for a country that has full diplomatic relations with Israel," Foreign Minister Avigdor Lieberman said in a statement.
One scene, broadcast on Israel’s Channel Two television on Wednesday, shows a Palestinian father holding a baby above his head and an Israeli soldier deliberately shooting the infant.
Israeli Prime Minister Benjamin Netanyahu said on Thursday of the tensions: "It of course raises the question of the direction of Turkish diplomacy. We hope it is in the direction of strengthening peace and not the extremist forces.
"I hope that what we are seeing here does not signal a fundamental change from the direction Turkey was heading until a year or two ago, and I hope we will return to work together ... to advance peace and security and prosperity in our region," he said at a news conference with Spanish Prime Minister Jose Luis Rodriguez Zapatero.
Turkey has recently strengthened relations with neighbouring Syria, where much of the Hamas leadership is based.
Israel’s three-week offensive in the Gaza Strip in December and January killed 1,417 Palestinians, including 926 civilians, a a Palestinian rights group says. Israel has said 709 Palestinian combatants were killed along with 295 civilians and 162 people whose status it was unable to clarify.
Ten Israeli soldiers and three civilians were killed during the campaign, which Israel launched with the declared aim of ending cross-border rocket attacks from the Gaza Strip.
During a meeting with the Turkish embassy charge d’affairs, a Foreign Ministry official said Israel "cannot stand by when such blatant incitement is being broadcast against Israel and (Israeli) soldiers", a statement issued by the ministry said.
The official also said the portrayal of Israeli soldiers as "a master race eager to murder children" could endanger Israeli and Jewish tourists who visit Turkey.
Turkish officials in Ankara and Tel Aviv were not immediately available for comment.
The show’s producer, Selcuk Cobanoglu, told Reuters: "If the Israeli government is disturbed with this, it means they are disturbed with the reality when we go there and eyewitness what is happening there."
Turkey barred Israel from participating in a NATO war exercise this week and Prime Minister Tayyip Erdogan said the move was a result of public concerns over the Israeli military campaign in the Gaza Strip.
The drill was postponed indefinitely after other nations, including the United States and Italy, refused to take part without Israel’s air force.
In January Erdogan, head of the Islamist-rooted AK Party, stormed out of a debate with Israeli President Shimon Peres at the World Economic Forum in Switzerland in protest at the Gaza offensive. (Additional reporting by Ibon Villelabeitia and Omer Berberogluin Ankara and Ari Rabinovitch in Jerusalem; editing by Andrew Roche)