The order comes after Russia accused Ukraine on Wednesday of launching a militant attack at "critically important infrastructure" near the city of Armyansk, Crimea, according to Russia's state news service TASS.
But Ukrainian President Petro Poroshenko refuted the claims, calling them "insane" and suggesting Russia's aim was more military threats against its neighbor.
The spat has seen tensions between the countries rise to their highest level since Russia annexed Crimea in 2014.
Violent clashes on the streets of Ukraine between pro-European activists and pro-Russian supporters in early 2014 set the scene for the annexation.
By March of that year, thousands of Russian-speaking troops poured into Crimea. Weeks later, Russia completed its annexation of the peninsula in a referendum that was slammed by Ukraine as illegitimate.
Fast forward to this week, with Russia's Federal Security Service claiming to have foiled a Ukraine-backed terror attack in Crimea, according to TASS.
The report said Russian forces spotted the "saboteurs" and while attempting to detain them, found "20 improvised explosive devices containing more than 40 kilograms of TNT equivalent, ammunition, fuses, antipersonnel and magnetic bombs, grenades and the Ukrainian armed forces' standard special weapons."
It said two Russian servicemen were killed in ensuing clashes.
Russian President Vladimir Putin held an urgent meeting with his security council to discuss additional measures in Crimea on Thursday, TASS reported. The country also announced naval exercises in the Black Sea for the next three days "to counter underwater saboteurs."
Ukraine has denied the attack, with President Poroshenko saying in a statement: "Russian accusations that Ukraine launched terror attacks in the occupied Crimea are equally cynical and insane as its claims there is no Russian troops in eastern Ukraine."
Ukrainian Security Services adviser Yuriy Tandit added that "Ukraine does not seize or return by force its territory now and will not do so in the future," in a statement reported by Interfax-Ukraine.
US Ambassador to Ukraine Geoffrey Pyatt also disputed Russia's claims, saying on his Twitter account
that: "Russia has a record of frequently levying false accusations at Ukraine to deflect attention from its own illegal actions."
He added that the US had so far seen no evidence to support Russia's accusations.
A NATO official also told CNN that Russia had provided no evidence for the accusations, adding that it was monitoring the situation closely.
"We are deeply concerned by the recent upsurge in violence in eastern Ukraine, and the increase in ceasefire violations along the line of contact, primarily by the Russian-backed militants," said the official.
"We call on Russia to reverse its illegal and illegitimate annexation of Crimea."