Kerry issued the warning in a phone call to Foreign Minister Sergei Lavrov on Wednesday, according to the US State Department.
Russian Foreign Ministry spokeswoman Maria Zakharova said Wednesday that there are "Russian military experts in Syria who are instructing (the Syrians) on the use of the military systems being delivered" to the Syrian government.
Russia "has long been supplying arms and military equipment to Syria in accordance with bilateral contracts," Zakharova said.
In his telephone call to Lavrov, the US secretary of state "reiterated our concern about these reports of Russian military activities, or buildup if you will, in Syria and made very clear our view that, if true and borne out, could lead to greater violence and even more instability in Syria," State Department spokesman John Kirby told reporters in Washington, DC.
Russia has dispatched a military advance team to Syria and is taking other steps to expand its military support for the government of President Bashar al-Assad, the New York Times has reported.
According to US intelligence analysts, Russia has also sent prefabricated housing units for hundreds of people to a Syrian airfield as well a portable air traffic station, the Times report said.
Syria has been gripped by deadly unrest since March 2011. According to reports, the United States and its regional allies - especially Qatar, Saudi Arabia, and Turkey - are supporting the militants operating inside the country.
According to the United Nations, more than 230,000 people have been killed and millions displaced due to the turmoil that has gripped Syria for over four years.
The Daesh (ISIL) terrorists, who were initially trained by the CIA in Jordan in 2012 to destabilize the Syrian government, now control large parts of Iraq and Syria.
Since late September 2014, the US and some of its Arab allies have been carrying out airstrikes against ISIL inside Syria without any authorization from Damascus or a UN mandate; Press TV reported.