The Black Sea port of Kherson has become the first major Ukrainian target to fall under the de facto control of Russia forces, as the United Nations said more than a million people had fled the country since the invasion began a week ago.

As the international criminal court said it had begun collecting evidence of possible war crimes in Ukraine, Kherson’s mayor, Igor Kolykhaiev, said in a Facebook post early on Thursday that Russian troops were in control of the city hall and that residents should obey a curfew imposed by what he called the “armed visitors”.

Amid conflicting reports about the fate of the strategically important city, Kolykhaiev said he had made “no promises” to the Russian forces and that he was “only interested in the normal life of our city! I just asked [them] not to shoot people”.

Other restrictions imposed on the city include a curfew from 8pm until 6am with only cars transporting food, medicines and other necessities permitted to enter the city.

The Russian attack on the city left bodies strewn about the city streets, power outages, limited water and little food, the New York Times reported Kolykhaiev as saying in a separate interview. A group of about 10 armed Russian officers entered the city hall and informed him that they planned to set up a military administration, the mayor added.

Gennady Lakhuta, head of the regional administration, wrote on the messaging service Telegram late on Wednesday that the city had been overrun by Russian troops. “The [Russian] occupiers are in all parts of the city and are very dangerous,” he said, according to Agence France-Presse.

Russian artillery and missiles have continued to bombard other major cities including the capital, Kyiv, and the second-biggest city, Kharkiv, where a Ukrainian member of the Organization for Security and Cooperation in Europe’s (OSCE) monitoring mission was killed in a bombing.

There is also still believed to be fierce fighting in the port of Mariupol in the country’s south-east where Ukrainian forces are surrounded by the Russian-aligned forces. “We cannot even take the wounded from the streets, from apartments, since the shelling does not stop,” its mayor said, adding that Russian attacks had been repelled “with dignity”.

Hundreds of civilians have been killed, according to UN estimates, although the real tally is feared to be much higher. Ukraine’s government said on Wednesday nearly 6,000 Russian troops had been killed. Moscow said the figure was 498.

As the conflict entered its second week the UN high commissioner for refugees, Filippo Grandi, said there had been an “exodus” from Ukraine to neighbouring countries of more than one million people, or around 2% of the population of 44 million.

Grandi appealed for the “guns to fall silent” so humanitarian aid could reach millions more still inside the country, and cautioned that the flood of people escaping the war was far from over and could eventually total 4 million.

In another dramatic development, the UK and 37 other countries formally referred reports of atrocities committed in Ukraine to the international criminal court (ICC) on Wednesday, the largest such referral in the court’s history.

Under ICC rules, such a referral from member states means the court’s prosecutor, Karim Khan, has already been able to start collecting evidence for the investigation without waiting for the approval of ICC judges.

Britain’s foreign secretary, Liz Truss, in statement: “Putin’s military machine is targeting civilians indiscriminately and tearing through towns across Ukraine. An investigation by the international criminal court into Russia’s barbaric acts is urgently needed and it is right that those responsible are held to account. The UK will work closely with allies to ensure justice is done.”

In New York, an emergency session of the UN general assembly voted overwhelmingly to deplore Russia’s invasion of Ukraine and called for the immediate withdrawal of its forces. Of the 193 member states, 141 voted for the resolution, 35 abstained, and five – Russia, Belarus, Syria, North Korea and Eritrea – voted against.

The resolution deplored Russian aggression against Ukraine “in the strongest terms” and demanded that “the Russian Federation immediately cease its use of force against Ukraine” and “immediately, completely and unconditionally withdraw all of its military forces”.

The resolution is not legally binding, but is an expression of the views of the UN membership, aimed at increasing pressure on Moscow and its ally, Belarus.

The OSCE named the killed member of its monitoring team as Maryna Fenina, who died in Kharkiv while collecting supplies for her family.

The city has come under intense shelling by Russian forces in recent days, with police and university buildings bombarded and government offices reduced to rubble.

“In Kharkiv and other cities and towns in Ukraine, missiles, shells and rockets are hitting residential buildings and town centers, killing and injuring innocent civilians – women, men and children alike,” the OSCE said.

“We strongly condemn the increased shelling in urban areas,” it added, reiterating its call “on the Russian Federation for an immediate cessation of hostilities”.

The international effort to isolate Russia and cripple its economy also continued when the World Bank said on Wednesday it had stopped all programs in Russia and Belarus with immediate effect.

Russian oligarch’s were also being squeezed as German authorities reportedly seized the $600m superyacht belonging to Russian billionaire Alisher Usmanov in a Hamburg shipyard. It came after Roman Abramovich put English football club Chelsea up for sale, nearly 20 years after he took control.

A second round of talks between Ukraine and Russia is due to get under way on Thursday, Russian negotiators reportedly said, adding that a ceasefire was “on the agenda”. However, Ukraine’s foreign minister, Dmytro Kuleba, has said Moscow’s demands are unacceptable and Russia must stop bombing cities if any progress is to be made.

The war again wreaked havoc on financial markets as the price of Brent crude oil soared to more than $117 a barrel on Thursday, marking a 20% rise this week. A range of other commodities such as aluminium, iron ore and wheat rose again, intensifying concerns that the global economy is going to be thrown off course by runaway inflation.