The minister indicated that Russian statements about its willingness to use nuclear weapons were alarming.
"I think that what we are witnessing is unprecedented since 1962, since [the] Cuban missile crisis," Reuters quoted Rinkēvičs as saying.
Rinkēvičs also believes that Moscow's nuclear rhetoric demonstrated the need for more NATO troops and equipment in the region, and that the military alliance must "be prepared for all kinds of contingencies."
A ceasefire agreement that was reached four months ago in Minsk reduced the scale of hostilities in eastern Ukraine, but clashes still occur and people die there every day. On Wednesday EU member states agreed to extend until January 31, 2016 their sanctions against Russia that have been imposed for its aggression in Ukraine.
Rinkēvičs said that violations of the peace deal had forced the extension of sanctions, and warned that escalating tensions there risked spiralling out of control.
"We cannot say that the Minsk agreement is totally broken, but what we have seen recently is that the level of tension is increasing," Rinkēvičs said.
"We are in a situation where [the] Minsk agreement can be broken anytime and in that case we are going to see [a] totally different situation, which is not going to be better," the Latvian minister said.
This week Russia announced it was adding 40 new intercontinental ballistic missiles to its nuclear arsenal, placing further strain on relations between Moscow and the West, already tense over the Ukraine crisis.