(Changes dateline, adds envoy return confirmation)
AMMAN, May 13 (Reuters) - Jordan's kidnapped ambassador to Libya has been freed by his captors, has left the country and is on his way home, a Jordanian cabinet minister said on Tuesday.
"Ambassador Itan is on his way home and in good health," Jordan's Foreign Minister Nasser Joudeh was quoted as saying on state television.
Earlier the pan-Arab news channel Al Arabiya Television said the Libyan foreign ministry had confirmed the release to it. Al Jazeera television also reported the news.
Ambassador Fawaz al-Itan was kidnapped last month by gunmen who demanded an Islamist militant be released from a Jordanian jail in exchange for the diplomat's freedom. There was no immediate indication whether that demand had been met.
But Libya's state news agency LANA had reported that Jordan had agreed to hand a Libyan Islamist to Tripoli to secure Itan's release.
Mohamed Dersi was jailed for life in 2007 for plotting to blow up the main airport in Jordan.
Analysts have said agreeing to the kidnappers' demand could set a dangerous precedent for Jordan, which is an important U.S. ally in the fight against al Qaeda.
Kidnappings have become commonplace in Libya, with foreign diplomats often the targets. (Writing by Yara Bayoumy, Additional reporting by Suleiman Khalidi; Editing by Clarence Fernandez)