Ukraine’s president, Volodymyr Zelenskiy, said the intensity of fire by Russian troops towards Kharkiv, the Donbas and in Dnipro has “increased significantly”, one day after the Kremlin launched its long-anticipated offensive in eastern Ukraine. Russian officials said a total of 1,260 military targets were hit by rockets and artillery along the 300-mile frontline in the Donbas and Kharkiv regions.

Zelenskiy said the situation in the besieged city of Mariupol is “as severe as possible”. “The Russian army is blocking any efforts to organise humanitarian corridors and save our people,” Zelenskiy said in his nightly address. “The fate of at least tens of thousands of Mariupol residents who were previously relocated to Russian-controlled territory is unknown.”

The Russian defence ministry said it would offer a ceasefire in Mariupol on Wednesday to allow Ukrainian defenders holed up in the Azovstal steelworks to lay down their arms. Russian-backed fighters have been storming the plant, according to a pro-Russian official cited by the BBC. Ukrainian authorities say that no fewer than 1,000 civilians are hiding in the complex along with Ukrainian fighters.

Russian forces have seized Kreminna in eastern Ukraine’s Donbas region and Ukrainian troops have withdrawn from the city, the regional governor said. Kreminna, a city of more than 18,000 people about 350 miles (560km) south-east of Kyiv, appears to be the first city captured in a Russian offensive in eastern Ukraine.

The mayor of Kharkiv, Ihor Terekhov, said Russian forces have been engaged in “non-stop bombardment of civilian districts” in Ukraine’s second city since Sunday. Four people, including three emergency workers, were killed on Tuesday, according to Terekhov. Separately, the prosecutor’s office for the Kharkiv region said Russian rockets wounded 14 people in the city on Tuesday.

A Russian businessman, Oleg Tinkov, has spoken out against the “crazy” war in Ukraine and described supporters of Moscow’s military actions as “morons”. In an Instagram post, Tinkov, who has been sanctioned by the UK government, said “90% of Russians are against” the war.

Russia has increased its offensive in the Donbas but its progress has been hampered by “environmental, logistical and technical challenges”, the UK said. “Russia’s inability to stamp out resistance in Mariupol and their indiscriminate attacks, which have harmed the resident civilian populace, are indicative of their continued failure to achieve their aims as quickly as they would like,” the UK Ministry of Defence said late on Tuesday.

Russia has deployed up to 20,000 mercenaries from Syria, Libya and elsewhere in Ukraine’s Donbas region, according to a European official. The official said mercenaries are being sent into battle with no heavy equipment or armoured vehicles.

In his nightly address, Zelenskiy claimed if Ukraine had access to all the weapons it needs, “and which are comparable to the weapons used by the Russian Federation, we would have already ended this war. It is unfair that Ukraine is still forced to ask for what its partners have been storing somewhere for years.”

The US president, Joe Biden, will announce another military aid package for Ukraine roughly the same size as the $800m one the US president announced last week, multiple sources told Reuters, which would bring to more than $3bn the total US aid to Ukraine since Russia’s invasion.

Russia is expelling 31 Dutch, Belgian and Austrian diplomats as Moscow faces increased international isolation. It comes after the Netherlands, Belgium and Austria announced the expulsion of some Russian diplomats.

The UN secretary general, António Guterres, has called for a four-day Orthodox Easter humanitarian pause in fighting in Ukraine. Guterres said the UN was ready to send humanitarian aid convoys to Mariupol, Kherson, Donetsk and Luhansk beginning on Holy Thursday and running through Sunday 24 April, the date of Orthodox Easter, which is celebrated by most Ukrainians and Russians.