The new security measures in the three Russian border regions were announced by the National Counter-Terrorism Committee (Nak) on Friday.
It said this was done “to ensure the safety of citizens and suppress the threat of terrorist acts by enemy sabotage and reconnaissance units”.
The authorities now have powers to enter private homes, restrict the movement of traffic and pedestrians, order the temporary relocation of people and monitor information sent electronically.
This comes as Moscow is struggling to contain the Ukrainian offensive.
More than 76,000 people have already been evacuated from the Kursk region’s border areas, according to Russia’s state Tass news agency.
Russia said that up to 1,000 Ukrainian troops, supported by tanks and armoured vehicles, entered the Kursk region on Tuesday morning.
The Ukrainians have since reportedly seized a number of villages, and are also threatening the regional town of Sudzha.
On Friday, a video emerged purportedly showing armed Ukrainian soldiers who claimed to have control over the town, as well as a key Russian gas facility there owned by the Gazprom company.
BBC Verify has now confirmed that the footage was indeed from the Gazprom facility on the north-western outskirts of Sudzha, about 7km from the border with Ukraine. The video alone does not verify the claim that Ukrainian troops have taken the whole town.
Russian military bloggers earlier claimed that the town was in Moscow’s hands.
Earlier, BBC Verify checked and confirmed the location of another video posted online on Friday morning. It shows a 15-vehicle Russian convoy damaged, burned and abandoned on a road through the town of Oktyabrskoe, roughly 38km from the border on the Russian side.
The footage also shows Russian soldiers, some injured, possibly dead among the vehicles.
Moscow has since sent reinforcements – including tanks and rocket-launching systems – to the Kursk region.
In its latest report on Saturday morning, the Russian defence ministry said its troops were “continuing to repel the attempted invasion” of Ukrainian forces.
It claimed that Ukraine’s attempts to “break through deep into Russian territory” had been foiled.
The Russian claims have not been independently verified.
On Friday, the UN nuclear agency urged both Russia and Ukraine to “exercise maximum restraint” as the fighting was edging closer to the Kursk nuclear power plant – one of the biggest such facilities in Russia.
International Atomic Energy Agency (IAEA) chief Rafael Grossi said measures must be taken “to avoid a nuclear accident with the potential for serious radiological consequences”.
The power plant is located about 60km north-east of Sudzha.
SOURCE: BBCNEWS