(Adds U.S. comment, paragraphs 5-6)

ANKARA, May 29 (Reuters) - Turkey asked the United States formally on Tuesday to avoid another violation of its airspace after an incident that exposed tensions between the NATO allies.

Last week, two U.S. F-16 warplanes briefly infringed Turkish airspace near the Iraqi border. U.S. diplomats say the incident was an "accident." Turkish media say it was intended to send a message to Ankara not to send its troops into northern Iraq.

"After we received detailed technical information from the General Staff on the incident, the necessary diplomatic initiative was made today in the presence of (a representative of) the U.S. embassy," the Foreign Ministry said in a statement.

A Turkish Foreign Ministry official told Reuters: "In the note given (to the embassy representative) it was requested that this kind of incident not be repeated."

In Washington, U.S. State Department spokesman Tom Casey told reporters the planes had inadvertently violated Turkish airspace for "a couple of minutes" and that the United States was investigating and would seek to prevent any recurrence.

"We are going to make sure we thoroughly look into this and make sure that there are no further incidents of this kind," he said. "Obviously we don't want to do anything that would violate Turkish airspace or infringe in any way on their rights."

The incident has coincided with increased media speculation in Turkey, which faces a national election in July, of a possible Turkish military incursion into northern Iraq to crush Turkish Kurdish rebels hiding there.

The rebels use northern Iraq as a springboard to attack military and security targets inside Turkey. Ankara has long urged U.S. and Iraqi forces to crack down on the rebels.

Foreign Minister Abdullah Gul said on Friday there were no preparations in parliament to give approval to send troops into Iraq. In its statement on Tuesday, the Foreign Ministry said it was working closely with the General Staff on the issue.

Turkish newspapers have suggested the two institutions have not been coordinating their actions. The General Staff recently helped prevent Gul, a former Islamist, being elected president in an election in parliament that has now been postponed. (Additional reporting by Arshad Mohammed in Washington)

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