The military authorities said on Tuesday that the Russian army is intensifying its attacks in eastern Ukraine, even as Kremlin forces are trying to curb a stunning week-long incursion into Russia by Kyiv's forces.

The Ukrainian General Staff said on Tuesday that in the past 24 hours, Russian forces launched 52 attacks in the Pokrovsk area, a town in the eastern Donetsk region near the front line. This represents double the daily attacks there about a week ago.

The Ukrainian army claims that its bold assault on Russian territory, which began on August 6, has already included about 1,000 square kilometers (386 square miles) of Russian land.

The goals of the rapid advance into the Kursk region are a closely guarded military secret.

However, analysts say the motivating factor may have been Ukraine's desire to ease pressure on the front line by trying to draw Kremlin forces into defending Kursk and other border areas. If that is the case, the increasing pressure around Pokrovsk suggests that Moscow has not taken the bait.

Nonetheless, the cross-border operation launched by Ukraine - the largest attack on Russia since World War II - has unsettled the Kremlin. It forced Russian President Vladimir Putin to hold a meeting on Monday with top defense officials.

It is clear that Ukraine has amassed thousands of troops - some Western analysts estimate their number to be around 10,000 to 12,000 soldiers - at the border in recent weeks without Russia noticing or doing anything about it.

Russian officials said that around 121,000 people had been evacuated from Kursk or fled from the combat-affected areas on their own. The Institute for the Study of War, a Washington-based research center, stated that it had seen geographic footage indicating that Ukrainian forces advanced up to 24 kilometers (15 miles) from the border.

The Russian Ministry of Defense appeared to support this claim when it said on Tuesday that it had repelled an attack by units of the 82nd Air Assault Brigade of the Ukrainian Armed Forces towards Marinka, which is approximately that distance from Ukraine.

Russian state television showed on Tuesday residents of evacuated areas lining up at buildings and on the street to receive food and water.

Volunteers were seen distributing bags of aid, while officials from the country's Emergency Ministry assisted people, including children and the elderly, in disembarking from buses.

An elderly man named Mikhail told Russian state television: "There is no light, no communication, no water. There is nothing. It's as if everyone flew to another planet, and you are left alone. The birds stopped singing, helicopters and planes flew over the yard, and shells were flying. What could we do? We left everything behind."

Putin stated that the impetus behind Ukraine's bold incursion into Russia was to incite unrest, but he said these efforts would fail.

The successful border breach was also surprising as Ukraine has been suffering from a manpower shortage at the front while waiting for new brigades to complete training.

Dara Masikout, an analyst at the Carnegie Endowment, said that the Ukrainian breakthrough was a clever move because it exploited gaps between the various Russian command structures in Kursk: border guards, Ministry of Defense forces, and Chechen units fighting alongside Russia in the war.

Masikout stated late on Monday that Russian command and control are divided in Kursk.

The Ukrainian General Staff announced on Tuesday that it had established a restricted access area 20 kilometers (12 miles) long along the Russian-Ukrainian border in the northeastern Sumy region bordering Kursk.

The statement said that the measures were taken due to the increasing intensity of fighting in the area and the growing presence of Russian reconnaissance and sabotage units in the region.