MOSCOW — The Russian defense minister on Thursday ordered a partial pullback of troops from the border with Ukraine, signaling a possible de-escalation in a military standoff that had raised alarm that a new war in Europe could be on the horizon.

The order came a day after President Vladimir V. Putin, in an annual state of the nation address, rattled off a list of grievances against Western nations, including threats of new sanctions. Mr. Putin warned against crossing a Russian “red line” with additional pressure on Moscow. The huge buildup on the Ukrainian border was in place while he spoke.

The defense minister, Sergei K. Shoigu, who had called the buildup a test of the Russian military’s readiness, said that the units deployed to the border area had shown their capabilities and should now return to their regular positions.

“I think the goals of the readiness test are achieved fully,” Mr. Shoigu said, according to the official Russian news agency Tass, which reported that he had ordered troops from central Russia and Siberia to return to their barracks by May 1.

However, the order specified that troops departing from one large field camp about 100 miles from the Ukrainian border should leave their armored vehicles there until the fall. Satellite images had shown hundreds of trucks and tanks parked in fields in the area.