NATO Secretary-General Jens Stoltenberg said in a statement: "(Thursday), the North Atlantic Council (NATO's political decision-making body) authorized the deployment of additional troops to cope with the situation."
The statement did not specify what troops could be deployed if necessary, but Britain's Ministry of Defence said a battalion of between 500 and 650 troops had been placed at Kfour disposal when necessary.
The British ministry added that the battalion had "finally arrived in the area" for long-scheduled exercises.
"We will always take all necessary measures to maintain a safe environment, as well as freedom of movement for all those living in Kosovo," Stoltenberg said.
In northern Kosovo, where the majority of the population is a Serb minority, KFOR has decided to "strengthen its presence and activity," according to a NATO official who asked not to be identified.
The official said KFOR had already strengthened its presence in Kosovo in May by deploying about 500 Turkish military personnel who were later replaced by Bulgarians and Greeks.
The official indicated that KFOR was ready to make "additional adjustments" if necessary, to enable it to carry out its peacekeeping mandate in Kosovo.
A Kosovo policeman was killed on Sunday in an ambush in northern Kosovo. This was followed by an exchange of fire between the Kosovo Police Special Forces and heavily armed Serb fighters.
This is the most serious escalation Kosovo has seen in recent years.
A White House spokesman said Friday that the United States was "calling on Serbia to withdraw its troops" deployed on the border with Kosovo, citing a strengthening of the NATO force presence in the former province.
White House National Security Council spokesman John Kirby said "we see a large Serbian military deployment along the border with Kosovo," including an "unprecedented" deployment of artillery batteries, tanks and infantry units.