"Air defense systems have worked over different regions of Crimea. Please remain calm and trust only verified sources of information," Kryuchkov said on Telegram on Saturday morning.
Traffic across the Crimean Bridge was temporarily suspended for about two hours during the night.
The Russian Defense Ministry subsequently confirmed that Ukrainian forces had attempted to carry out an attack using 20 drones, all of which were destroyed.
"Tonight, an attempt by the Kiev regime to carry out a terrorist attack using 20 unmanned aerial vehicles [UAVs] on sites on the territory of the Crimean peninsula was thwarted," the ministry said in a statement.
The ministry specified that 14 Ukrainian drones were destroyed by Russian air defense systems, while another six UAVs were suppressed by means of electronic warfare.
There are no casualties or damage as a result of the attempted attack, the defense ministry said.
The alerts were issued as reports emerged that Russian forces successfully repelled several strikes by Ukrainian forces near Kupyansk.
"During the day, the enemy carried out four counterattacks with units of the 14th and 41st separate mechanized brigades and the 25th separate airborne brigade on the positions of our troops in the area of the village of Sinkovka … All counterattacks were successfully repelled. Enemy losses amounted to a platoon of manpower," the spokesperson said.
The spokesperson added that Ukrainian troops have also attempted to carry out three attacks in the Svatovo region, but Russian troops successfully repelled the attacks.
"In the course of hostilities in the Kupyansk direction, the [Russian] assault groups … captured four [Ukrainian] strongholds and five observation posts," the spokesperson told Sputnik.
The latest reports of activity surrounding Kupyansk come as Russian forces have been making steady advances since mid-July. It was recently noted Russian troops moved forward some 11 kilometers along the frontlines as forces were able to liberate five settlements in the area.