LVIV, Ukraine — Russia announced yet another limited cease-fire and the establishment of safe corridors to allow civilians to flee some besieged Ukrainian cities Monday. But the evacuation routes led mostly to Russia and its ally Belarus, drawing withering criticism from Ukraine and others.

Ukrainian officials accused Moscow of resorting to “medieval siege” tactics in places, and in one of the most desperate of the encircled cities, the southern port of Mariupol, there were no immediate signs of an evacuation.

Russian President Vladimir Putin’s forces continued to pummel some cities with rockets even after the announcement of corridors, and fierce fighting raged in places, indicating there would be no wider cessation of hostilities.

Efforts to set up safe passage for civilians over the weekend fell apart amid continued shelling. But the Russian Defense Ministry announced a new push Monday, saying civilians would be allowed to leave the capital of Kyiv, Mariupol and the cities of Kharkiv and Sumy.

The two sides met for a third round of talks Monday, according to Russian state media, though hopes for any breakthrough were dim. The countries’ foreign ministers are also scheduled to meet in Turkey on Thursday, according to that country’s top diplomat.

Ukrainians, whose ferocious resistance has slowed the invasion and thwarted any hopes Moscow had for a lightning victory, have been reinforcing cities across the country.

In Kyiv, soldiers and volunteers have built hundreds of checkpoints, often using sandbags, stacked tires and spiked cables. Some barriers looked significant, with heavy concrete slabs and sandbags piled more than two stories high, while others appeared more haphazard, with hundreds of books used to weigh down stacks of tires.

“Every house, every street, every checkpoint, we will fight to the death if necessary,” said Mayor Vitali Klitschko.

Dozens of makeshift kitchens are serving food to soldiers.

“I’m carrying out my duty, working for my country, thanking our soldiers,” Natalia Antonovska said at one kitchen. “That’s why I’m here, and I’m very proud of it.”

In Kharkiv, heavy shelling slammed into apartment buildings Monday.

“I think it struck the fourth floor under us,” Dmitry Sedorenko said from his Kharkiv hospital bed. “Immediately, everything started burning and falling apart.” When the floor collapsed beneath him, he crawled out through the third floor, past the bodies of some of his neighbors.

In Mariupol, where an estimated 200,000 people hoping to flee were becoming increasingly desperate, Red Cross officials waited to hear when a safe corridor would be established. The city is short on water, food and power, and cellphone networks are down. Stores have been looted as residents search for essential goods.

Police moved through the city, advising people to remain in shelters until they heard official messages broadcast over loudspeakers to evacuate.

Hospitals in Mariupol are facing desperate shortages of antibiotics and painkillers, and doctors performed some emergency procedures without them.

The lack of phone service left anxious citizens approaching strangers to ask if they knew relatives living in other parts of the city and whether they were safe.

At the International Court of Justice at The Hague, Netherlands, Ukraine pleaded for an order to halt Russia’s invasion, saying Moscow is committing widespread war crimes and “resorting to tactics reminiscent of medieval siege warfare.” Russia snubbed the proceedings, leaving its seats in the Great Hall of Justice empty.

Well into the second week of the war, Russian troops have made significant advances in southern Ukraine and along the coast, but other efforts have become stalled, including an immense military column that has been almost motionless for days north of Kyiv.

The battle for Mariupol is crucial because its capture could allow Moscow to establish a land corridor to Crimea, which Russia seized from Ukraine in 2014.

The fighting has sent energy prices surging worldwide and stocks plummeting, and threatens t he food supply and livelihoods of people around the globe who rely on crops farmed in the fertile Black Sea region.

The U.N. human rights office reported 406 confirmed civilian deaths but said the number is a vast undercount. The invasion has also sent 1.7 million people fleeing Ukraine.

Ukrainian Deputy Prime Minister Irina Vereshchuk blasted the latest cease-fire proposal, which had most evacuation routes heading toward Russia or its ally Belarus, calling it “unacceptable.” Belarus served as a launching ground for the invasion.

French President Emmanuel Macron also dismissed the plan as a cynical move by Moscow.

“I don’t know many Ukrainians who want to seek refuge in Russia. That’s hypocrisy,” he said in an interview on French news broadcaster LCI.

The Ukrainian government instead proposed eight routes allowing civilians to travel to western regions of Ukraine where there is no shelling.

Earlier, Klitschko said in a Telegram video address that “fierce battles” continued Monday in the Kyiv region, notably around Bucha, Hostomel, Vorzel and Irpin.

In the Irpin area, which has been cut off from electricity, water and heat for three days, witnesses saw at least three tanks Monday and said Russian soldiers were seizing houses and cars.

A few miles away, in the small town of Horenka, where shelling reduced one area to ashes and shards of glass, rescuers and residents picked through the ruins as chickens pecked around them.

“What are they doing?” Vasyl Oksak, a rescue worker, asked of the Russian attackers. “There were two little kids and two elderly people living here. Come in and see what they have done.”

Russian forces also continued their offensive in Mykolaiv, opening fire on the city some 480 kilometers (300 miles) south of Kyiv, according to Ukraine’s military. Rescuers said they were putting out fires caused by rocket attacks in residential areas.

Emergency officials in the Kharkiv region said overnight shelling killed at least eight people and wrecked residential buildings, medical and education facilities and administrative buildings.

Russia has grown increasingly isolated in the face of punishing sanctions. The ruble’s value has plunged, and the country’s extensive business ties with the West have been all but severed.

Moscow has also cracked down on independent reporting on the conflict and arrested anti-war protesters en masse. On Sunday more than 5,000 people in 69 cities were detained, according to rights group OVD-Info — the highest single-day figure since the invasion began.

Ukrainian President Volodymyr Zelenskyy called for more punitive measures, including a global boycott of Russia’s oil exports, which are key to its economy.

“If (Russia) doesn’t want to abide by civilized rules, then they shouldn’t receive goods and services from civilization,” he said in a video address.

Russia’s invasion has nearby countries terrified that the violence could spread.

U.S. Secretary of State Antony Blinken on Monday began a lightning visit to the three Baltic states of Latvia, Lithuania and Estonia, former Soviet republics that are NATO members. Blinken hoped to reassure them of the alliance’s protection.

The West has rushed weapons to Ukraine, but NATO has shown no interest in sending troops into the country and has rejected Zelenskyy’s pleas to establish a no-fly zone for fear that could trigger a wider war.