The defence ministry announced the drills and also said Russian forces had captured two villages in eastern Ukraine, where outgunned and outmanned Ukrainian troops have been struggling to hold their positions.
Officials in the border region of Belgorod meanwhile said that Ukrainian aerial attacks had left at least seven people dead and wounded over 30, including several children.
Putin, who ordered the nuclear drills, has upped his nuclear rhetoric since ordering his army into Ukraine in 2022, warning in February there was a "real" risk of nuclear war.
The defence ministry gave no date for the exercises, but said they would involve the air force, navy and troops stationed near Ukraine.
It said they were aimed at ensuring Russian territorial integrity in the face of Western "threats."
The Kremlin specified that the exercises were a response to statements by French President Emmanuel Macron and British officials.
Russia has in recent days hit out at Macron for telling The Economist magazine he was "not ruling anything out" in the West's response to the conflict in Ukraine, including sending troops to the country.
It has also blasted UK Foreign Secretary David Cameron for saying Kyiv has the right to strike targets inside Russia.
- 'Dangerous rhetoric' -
"They are talking about the readiness and even the intention of sending armed contingents to Ukraine -- that is, in fact, to put NATO soldiers in front of the Russian military," Kremlin spokesman Dmitry Peskov said.
"This is a completely new round of escalating tensions. It is unprecedented and requires special measures," he added.
The Russian foreign ministry meanwhile said it had summoned the UK's ambassador in Moscow and warned him that if Ukraine used British weapons to attack Russia, that Moscow could hit UK military targets in Ukraine "and beyond."
It also summoned France's envoy after "increasingly belligerent statements" by Paris, following Macron's comments.
"The Russian side presented its assessment that Paris's destructive and provocative line is leading to an escalation of the conflict".
Ukrainian forces have been dependent on Western military aid to battle Russia but NATO has said it will not send troops into Ukraine.
Russia's defence ministry said troops from the Southern Military District, which borders Ukraine and includes the occupied Ukrainian territories, will take part in the drills.
"During the exercise, a set of measures will be taken to practise the preparation and use of non-strategic nuclear weapons," it said in a statement.
Non-strategic nuclear weapons, also known as tactical nuclear weapons, are designed for use on the battlefield and can be delivered via missiles.
- Deadly Belgorod attack -
In Russia's frontier Belgorod region -- under attack for months -- governor Vyacheslav Gladkov said two moving vans and a passenger car "came under attack by Ukrainian kamikaze-drones."
Six people were killed, he said, adding that 35 others were wounded in the attack near the village of Berezyovka -- some 30 kilometres (18 miles) from the Ukraine border.
Local authorities said the vehicles belonged to a meat production facility.
Gladkov said two children were among the wounded and that one man was in "serious condition" and undergoing surgery.
He later said another resident of the region had been killed in a separate Ukrainian bombardment of an outdoor cooking area.
Moscow has been making steady gains in eastern Ukraine and stepped up aerial attacks and shelling on border regions as Ukrainian force await the arrival of much-needed US military aid.
The defence ministry said its forces had "liberated the village of Kotlyarivka in the Kharkiv region" and the "village of Soloviove in the Donetsk People's Republic".
Kyiv said overnight Russian strikes had targeted energy facilities in the northern Sumy region and northeastern Kharkiv region -- both of which have seen increased attacks for weeks.
Hundreds of thousands of homes were temporarily left without power in the aftermath of the strikes, the Ukrainian energy ministry said.
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