JERUSALEM, Oct 15 (Reuters) - A Turkish television drama series depicting an Israeli soldier shooting dead a Palestinian baby put more strain on Thursday on relations between Israel and Turkey, a Muslim strategic ally.

Previously close ties between the Jewish state and Muslim Turkey have deteriorated somewhat since Israel's offensive in the Palestinian Gaza strip. Turkey has at the same time strengthened its relations with neighbouring Syria.

Israel summoned a Turkish diplomat to protest at what it called "state-sponsored incitement" by 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.

The scene, broadcast on Israel's Channel Two television on Wednesday, shows a Palestinian father holding a baby up above his head and an Israeli soldier in full combat gear taking aim and shooting the infant.

A Foreign Ministry spokesman said Israel summoned the deputy chief of mission at the Turkish embassy to protest at the "highly inflammatory" scenes aired on state-owned TRT.

Turkish officials in Ankara and Tel Aviv were not immediately available for comment.

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 offensive in the Gaza Strip earlier this year.

The drill was postponed indefinitely after other nations, including the United States and Italy, refused to take part without Israel's air force.

Turkey, a secular state with a Muslim population, has been a key strategic ally of Israel, but relations have cooled over Erdogan's outspoken criticism of Israel's three-week offensive in the Hamas-ruled Gaza Strip in December and January. (Additional reporting by Ibon Villelabeitia in Ankara; Editing by xx)