In a first public admission that Russia's invasion of Ukraine may not be going as planned, President Vladimir Putin has said the situation in four Moscow-annexed areas of Ukraine was proving "extremely difficult."

He also called for an increase in surveillance in his comments to mark Security Services Day in Russia on Tuesday. They followed a visit to close ally Belarus that fueled fears, dismissed by the Kremlin, that the country could help Russia open a new invasion front against Ukraine.

"The situation in the Donetsk and Lugansk People's Republics, in the Kherson and Zaporizhzhia regions, is extremely difficult," Putin told the Russian security services on their professional holiday.

Putin singled out those working in the "new regions of Russia."

"The people living there, the citizens of Russia, rely on you, on your protection," he said.

Putin also said that "maximum composure, the concentration of forces" was required of Russia's counterintelligence operations.

He ordered the Federal Security Services (FSB) to step up surveillance of Russian society and the country's borders to combat the "emergence of new threats" from abroad and traitors at home.

"It is necessary to strictly suppress the actions of foreign intelligence services, to quickly identify traitors, spies and saboteurs," he said.

Putin in September announced the Russian annexation of four territories in the east and south of Ukraine after Moscow proxies held referendums there, denounced as a sham by Kyiv and the West.

Kyiv calls for more weapons

Kyiv, meanwhile, was seeking more weapons from the West after weeks of attacks on energy facilities which have knocked out both power and water supplies amid freezing temperatures.

"Weapons, shells, new defense capabilities ... everything that will give us the ability to speed up the end to this war," President Volodymyr Zelenskyy said in his evening address.

Ukraine's military said it had shot down 30 of 35 "kamikaze" drones fired by Russia on Monday, mostly at the capital Kyiv. The unmanned aircraft fly towards their target, then plummet and detonate on impact.

Ukrainian officials said on Tuesday that five people had been killed in the eastern Donetsk and southern Kherson regions, with eight wounded, and that 21 missiles had knocked out power in the southern city of Zaporizhzhia.

Belarus activity

To the northwest of Ukraine, there has been constant Russian and Belarusian military activity for months in Belarus, which Moscow's troops used as a launch pad for their abortive attack on Kyiv in February.

Lukashenko has said repeatedly he has no intention of sending his country's troops into Ukraine. But the commander of Ukraine's joint forces, Lieutenant General Serhiy Nayev, said his country was prepared.

"The level of the military threat is increasing, but we are taking adequate measures," he was quoted as saying by the defense ministry on Telegram. "The Armed Forces' General Staff provides for the expansion of units in the event of a significant increase in the other side's forces."

The Kremlin on Monday dismissed the suggestion that Putin wanted to push Belarus into a more active role. The RIA Novosti news agency quoted Kremlin spokesperson Dmitry Peskov as saying such reports were "groundless" and "stupid".

Both Putin and Lukashenko were also at pains to dismiss the idea of Russia annexing or absorbing Belarus.

"Russia has no interest in absorbing anyone," Putin said.

Asked about this comment, U.S. State Department spokesperson Ned Price said it should be treated as the "height of irony," given it was "coming from a leader who is seeking at the present moment, right now, to violently absorb his other peaceful next-door neighbor."

Fighting grinds on

The 10-month-old conflict in Ukraine, the largest in Europe since World War II, has killed tens of thousands of people, driven millions from their homes and reduced cities to ruins.

Ukraine's General Staff said Russian artillery hammered 25 towns and villages around Bakhmut and Avdiivka in the east and several areas around Kupiansk, a northeastern town retaken by Ukraine in September.

Alexei Kulemzin, the Russian-installed mayor of the city of Donetsk, said Ukrainian shelling hit a hospital wing, along with a kindergarten, posting on Telegraph a photo of what appeared to be a waiting room with smashed furniture and fittings.

Reuters could not independently verify the battlefield accounts of either side.

Russia says it is waging a "special military operation" in Ukraine to rid it of nationalists and protect Russian-speaking communities. Ukraine and the West describe the Kremlin's actions as an unprovoked war of aggression.