* Government appears likely culprit of Houla massacre
* Pillay urges strengthening of UN mission's mandate
* French envoy says UN mission may be downgraded (Adds quotes, details, French envoy)
By Louis Charbonneau
UNITED NATIONS, July 2 (Reuters) - The Syrian government and the rebels are receiving more and more weapons, which is fueling violence in a 16-month conflict that the United Nations says has killed more than 10,000 people, U.N. human rights chief Navi Pillay said on Monday.
"The ongoing provision of arms to the Syrian government and to its opponents feeds additional violence," Pillay said in the written text of remarks she made to the U.N. Security Council. "Any further militarization of the conflict must be avoided at all costs."
"There is a risk of escalation," she told reporters after the closed-door meeting.
Pillay said she was now calling the situation in Syria "a non-international internal armed conflict," the legal term for a civil war. Once that term is used, diplomats say, it means the Geneva Conventions on armed conflict apply.
She did not say where the weapons were coming from, though Russia and Iran are among the Syrian government's key suppliers. U.N. diplomats say Qatar and Saudi Arabia have been transferring arms to Syria's increasingly militarized opposition.
Pillay reiterated her position that the 15-nation council should refer the issue of Syria's conflict to the International Criminal Court in The Hague because there crimes against humanity and other war crimes may have been committed.
She said both sides appear to have committed war crimes.
Pillay touched on the U.N. Human Rights Council's commission of inquiry's position on a massacre of more than 100 people in Houla in May. The commission said on Friday that forces loyal to Assad may have carried out many of the killings.
Pillay said there was evidence pointing to "the greater responsibility of the government."
She told the council that her office "cannot exclude the possibility that some of the killings were perpetrated by armed opponents (of the government)."
But she added that the "the bulk of the information gathered to date points to the involvement of government-supported Shabbiha militia responsible for many of the killings, and the use of indiscriminate fire of heavy weapons by the government."
The mandate of the U.N. observer mission in Syria is set to expire on July 20. Council diplomats say that one of the most likely scenarios, given the escalating violence and lack of a viable political process, is to reduce or eliminate the unarmed military observers and keep only a largely civilian operation.
French U.N. Ambassador Gerard Araud said one of the options under consideration was to "downgrade" the observer mission, known as UNSMIS.
Pillay, however, urged the council to take the opposite approach and strengthen the mission's mandate. The Arab League has called on the United Nations to increase the size of the 300-strong monitoring force, possibly making them peacekeepers by giving them arms to protect themselves and Syrian civilians.
"An UNSMIS presence in the country remains vital," she said. "While considering its reconfiguration, I urge this council to support and strengthen UNSMIS' mandate to enable it to effectively monitor and report on the human rights situation in Syria."
UNSMIS, which was deployed to monitor international mediator Kofi Annan's April 12 ceasefire plan that never took hold, suspended most of its operations on June 16 due to the violence.
This weekend's meeting of major powers on Syria in Geneva produced an agreement on a possible unity government in Damascus, though council diplomats said privately they were skeptical about whether it would have any impact on the ground.
Araud said the Geneva agreement was "the utmost we could get given the divisions within the international community."
Syria's ally Russia, along with China, have vetoed two Security Council resolutions criticizing the Syrian government and threatening it with possible U.N. sanctions. (Additional reporting by Michelle Nichols; Editing by Sandra Maler and Cynthia Osterman)