Turkey and Greece have agreed to cancel rival military exercises that were to have been held next week on their respective national days, NATO's Secretary-General Jens Stoltenberg said Friday.

The neighbours, while NATO members, are at loggerheads over energy drilling and maritime rights in the eastern Mediterranean and the alliance has set up a hotline to head off accidental clashes.

"This is a very welcome step," Stoltenberg said after a videoconference of NATO defence ministers, including Greece's Nikos Panagiotopoulos and Turkey's Hulusi Akar.

"These are steps in the right direction, and it helps to reduce the risks for instance and accidents."

Greece had been expected to conduct exercises on Wednesday October 28, its Oxi Day holiday, and Turkey on Thursday, celebrated there as Republic Day.

Turkey has deployed the Oruc Reis, a gas exploration vessel under military escort into Greek waters off the island of Kastellorizo, and Greek vessels are nearby.

Addressing a news conference after two days of talks on a variety of topics, Stoltenberg confirmed he had raised the situation with the Greek and Turkish ministers.   

"I will say that we had a good and constructive talks and allies expressed a strong support for the NATO de-confliction mechanism," Stoltenberg said. 

"I welcome now the fact that we have been able to see some concrete steps in that direction with the cancellation of the two exercises."

Stoltenberg also welcomed Germany's diplomatic mediation in the underlying dispute.

On Thursday, he had warned that -- while NATO could help keep the rival militaries apart -- it would be down to Ankara and Athens to open a dialogue to resolve their long-standing differences.