ISTANBUL, Dec 15 (Reuters) - Syrian rebel leaders said they would do all they could to protect journalists but were hampered by infighting, after international news organisations complained kidnappings were preventing full media coverage of the civil war.

In a letter over the weekend, the western-backed Supreme Military Council (SMC), which is in charge of the rebel Free Syrian Army (FSA), said it would seek to free all journalists who have been abducted.

At least 30 journalists are estimated by media organisations to be being held.

The SMC is the main body representing moderate rebel fighters but it has no sway over extremist groups suspected of carrying out abductions.

"It is imperative that we reiterate that the FSA, along with all of its units and brigades, will do its utmost to protect and support journalists in order that they can fulfil their vital work," a letter from the SMC said.

On Wednesday editors from 13 media companies, including Reuters, called on Syrian rebel leaders to stop armed groups kidnapping journalists.

Kidnappings are common in rebel-held northern areas around Aleppo, Idlib and Raqqa. The Committee to Protect Journalists has recorded at least seven abductions in the past two months alone.

Despite a series of groups defecting and forming their own alliances, the SMC remains the main rebel coalition but brigades aligned with it have their own identities and separate commands.

The SMC said it would try to ensure the letter is sent to "all unit commanders and brigades operating within Syria, who share in the values of freedom, justice and democracy".

But it added: "We are today, however, facing the challenges of infighting in some of the liberated areas and in a number of areas we face ongoing clashes with the regime and the militia groups who support it."

(Reporting by Dasha Afanasieva; Editing by Daren Butler and Philippa Fletcher)