(Adds quotes, foreign ministry statement)

ANKARA, April 14 (Reuters) - Iran informed Turkey in advance of its planned operation against Israel, a Turkish diplomatic source told Reuters on Sunday, adding that Washington had conveyed to Tehran via Ankara that any action it took had to be "within certain limits".

Turkey, which has denounced Israel for its campaign on Gaza, said earlier on Sunday that it did not want a further escalation of tensions in the region.

The Turkish source, speaking on condition of anonymity, said Turkish Foreign Minister Hakan Fidan had spoken to both his U.S. and Iranian counterparts in the past week to discuss the planned Iranian operation, adding Ankara had been made aware of possible developments.

Earlier this week, U.S. Secretary of State Antony Blinken spoke to Fidan to make clear that escalation in the Middle East was not in anyone's interest.

"Iran informed us in advance of what would happen. Possible developments also came up during the meeting with Blinken, and they (the U.S.) conveyed to Iran through us that this reaction must be within certain limits," the source said.

"In response, Iran said the reaction would be a response to Israel's attack on its embassy in Damascus and that it would not go beyond this."

Iran, which neighbours Turkey, had vowed retaliation for what it called an Israeli strike on its Damascus consulate on April 1 that killed seven officers of the Islamic Revolutionary Guard Corps.

Turkey's foreign ministry later confirmed the contacts in a statement, saying Ankara had called for restraint and warned of a regional war if tensions escalated further.

It said Ankara would continue efforts to prevent further conflict and escalation in the region.

A Turkish security source said CIA chief William Burns had spoken to Ibrahim Kalin, head of Turkey's MIT intelligence agency, over the Eid al-Fitr holidays and asked him to act as a "mediator" in the Israel-Iran tensions.

The two discussed ceasefire efforts in Gaza as well, the source said, without elaborating. (Reporting by Tuvan Gumrukcu; Additional reporting by Ece Toksabay; Editing by Alex Richardson and Jan Harvey)