* Russia says alarmed by "militarisation' of Turkey-Syria frontier
* NATO chief says Russian criticism not justified, move defensive
* France says backs Turkey's request for Patriot missiles
By Gabriela Baczynska and Martin de Sa'Pinto
MOSCOW/ZURICH, Nov 22 (Reuters) - NATO chief Anders Fogh Rasmussen rejected Russian criticism on Thursday of the alliance's possible deployment of Patriot missiles near Turkey's border with Syria.
Russia said earlier it opposed the deployment of the surface-to-air missiles, which Ankara has asked NATO for because it fears spillover from the civil war in its neighbour.
"This would not foster stability in the region," Foreign Ministry spokesman Alexander Lukashevich said.
Rasmussen, who was greeted by 100 anti-NATO protesters when he arrived to give a speech at the University of Zurich, said Russia's criticism was "not justified".
"We have made clear from the outset we will do what it takes to defend our ally Turkey," he said in answer to a question.
Rasmussen said the deployment of the Patriot missiles, which can be used to intercept missiles or planes, would "serve as a deterrent to possible enemies even thinking of attacks" and help "preserve stability along our southern borders". The move would be "purely defensive", he said.
Rasmussen, making the first visit to neutral Switzerland by a NATO secretary-general since 2004, voiced great concern about the situation on the Turkish-Syrian border and said "the Turks are increasingly worried about the situation".
NATO ambassadors met on Wednesday to consider Turkey's request, which followed weeks of talks between Ankara and NATO allies about how to shore up security on its 900-km (560-mile) border with Syria.
The ambassadors reached no decision but the three countries that could supply the Patriots, the United States, Germany and the Netherlands, all said they viewed Turkey's request positively, according to one NATO diplomat, who said a final decision to deploy missiles was unlikely before next week.
French Foreign Minister Laurent Fabius said in Paris on Thursday that France backed Turkey's request. "There is no reason to object, it is purely defensive," he told BFM TV.
Turkey has repeatedly scrambled fighter jets along the frontier and responded in kind to stray shells flying into its territory during the conflict in Syria, where an estimated 38,000 people have been killed since an uprising against President Bashar al-Assad's government began in March 2011.
"The militarisation of the Syrian-Turkish border is an alarming signal," Russia's Lukashevich told a weekly briefing.
"Our advice to our Turkish colleagues consists of something else entirely: to use its potential influence on the Syrian opposition to seek the start of an inter-Syrian dialogue as swiftly as possible, and not to flex muscles and move the situation in such a dangerous direction," he said.
Russia has vetoed three U.N. Security Council resolutions aimed at putting pressure on Assad and accuses the West of encouraging militants fighting his government.
Russia denies trying to prop up Assad, whose nation has been an avid buyer of its weapons and hosts a naval supply facility that is Moscow's only military base outside the ex-Soviet Union.
It says the crisis in Syria must be resolved without foreign interference, particularly military intervention, and that Assad's exit from power should not be imposed as a precondition for a political solution.
NATO was Moscow's Cold War opponent and Russia has repeatedly expressed concern about deployments relatively close to its borders by the Western alliance, which has expanded to include several former Soviet satellites and republics.