Russia declared Tuesday a temporary cease-fire in five besieged cities of Ukraine, including the capital, to let civilians leave.

"For safe evacuation of civilians from populated areas, a cease-fire is declared and humanitarian corridors are opening from Kyiv, Chernihiv, Sumy, Kharkiv, and Mariupol from 10:00 a.m. today," Russian Ministry of Defense spokesman Igor Konashenkov said at a press briefing.

All five cities except Kyiv had sustained brutal, indiscriminate bombardment in recent days.

It's the fourth attempt to hold fire and allow civilians to escape the onslaught since Russian forces invaded Ukraine on Feb. 24. Russian and Ukrainian negotiators have been holding talks in recent days, and the Russian delegation has previously agreed to a temporary cease-fire and opening of humanitarian corridors in parts of Ukraine. But Russia has violated its own cease-fire and shelled evacuation points, while falsely accusing Ukraine of using people as human shields.

The hard-hit cities of Kharkiv and Mariupol were reported to be quiet Tuesday morning, with a local official telling ABC News that the center of Mariupol, a strategic port in the southeast, is not being shelled for the first time in days.

Ukraine said Russia has agreed this time to allow civilians to evacuate not only to Russia but also to other parts of Ukraine. Columns of buses and trucks with humanitarian aid are currently headed to Sumy, Mariupol and possibly other cities.

Ukrainian Deputy Prime Minister Iryna Vereshchuk said Russia has confirmed to the International Committee of the Red Cross that one route out of Sumy will be open. Vereshchuk said she hopes Russia will confirm routes for the other cities and also for the eastern city of Volnovakha. She warned Ukraine has information that Russia may have plans to disrupt the evacuations by leading civilians out of the agreed safe routes, in order to claim that Ukraine is not observing the agreement.

Petro Andrushenko, advisor to the mayor of Mariupol, said the city plans to evacuate people as long as Russian forces do not fire. A column of 60 buses and nine trucks of medical aid and food are headed to Mariupol now, and the hope is that at least 4,000 people can be evacuated via the buses plus an unknown number of private cars that will join the convoy, according to Andrushenko.

"If Russia doesn’t break it, we plan to evacuate people," Andrushenko told ABC News via telephone Tuesday morning.

-ABC News' Julia Drozd and Patrick Reevell

The World Bank said its board approved a package of loans and guarantees for Ukraine totalling $723 million.

The funding will help the Ukrainian government pay for government services, “including wages for hospital workers, pensions for the elderly, and social programs for the vulnerable,” the bank said in a statement on Monday.

The bank said it's preparing an additional $3 billion in support for Ukraine and neighboring countries, which have taken in more than 1.7 million refugees since the Russian invasion began.

“The World Bank Group is taking quick action to support Ukraine and its people in the face of the violence and extreme disruption caused by the Russian invasion,” World Bank President David Malpass said in a statement. “The World Bank Group stands with the people of Ukraine and the region. This is the first of many steps we are taking to help.”

The funding announced on Monday includes $350 million in supplemental loans, along with guarantees totalling $139 million from the Netherlands and Sweden, the bank said. Grant financing totalling $134 million will come from the United Kingdom, Denmark, Latvia, Lithuania and Iceland. Japan is providing $100 million in additional financing, the bank said.

There have been monumental efforts, especially by Poland, to get weapons into Ukraine and to the front lines.

But a senior official told ABC News there are indications Russia may attack one of those supply chains in Poland before it gets to Ukraine, potentially using air power.

Russian forces have created heavily fortified areas from which to launch long-range artillery, the official said, meaning they can shell cities from a distance rather than send troops into them. Ukrainian President Volodymyr Zelenskyy has repeatedly requested air power assistance in order to destroy these fortified areas.

Ukrainians have seen success in attacking Russian resupply areas, mostly in the north but also among smaller, moving groups.

-ABC News' Martha Raddatz

Ukrainian President Volodymyr Zelenskyy has filmed himself from the street just outside his office, but for the first time since the invasion began, he posted a video message from inside.

“We’re not scared, because you’re not scared,” he told Ukrainians who have taken up arms and told Russia it is not welcome.

“So, I stay here at Bankova Street,” Zelenskyy said. “I’m not hiding from anyone and not afraid of anyone as long as it takes to win in this war, our truly patriotic war.”

The latest address was filmed as a selfie in which he showed a view of Kyiv on Monday night.

“This is Kyiv at night outside the window. This is our office. Monday night. You know, we’re used to saying Monday is a hard day,” he said. “But the country is at war now, so every day is Monday.”

-ABC News’ Christine Theodorou