Ukraine’s troops have withdrawn from several areas of the country’s north-east amid mounting pressure from a new Russian offensive, as the president, Volodymyr Zelenskiy, postponed all foreign trips underscoring the seriousness of the threat. The moves came as the Russian president, Vladimir Putin, said Moscow’s latest operation was “going to plan” and Russian forces were improving their positions daily even as the US rushed to resupply arms and ammunition to Kyiv. Ukrainian military said late on Tuesday that troops fell back from areas in Lukyantsi and Vovchansk near Kharkiv “to save the lives of our servicemen and avoid losses”. Moscow launched a surprise major ground assault on the Kharkiv region last week as it sought to advance while Kyiv is struggling for arms and manpower. Zelenskiy said in his nightly video address on Tuesday that the army had sent reinforcements to the Kharkiv and Donetsk regions. “It is too early to draw conclusions, but the situation is under control,” he said. Ukraine’s president had been expected to visit Spain, and perhaps Portugal, later this week but cancelled all foreign visits. Against the backdrop of renewed Russian pressure, the US secretary of state, Antony Blinken, sought to reassure the ally of continuing American support, announcing a $2bn arms deal. The United States is rushing ammunition, armoured vehicles, missiles and air defences to Ukraine to ensure their speedy delivery to the frontline, added Blinken on Wednesday. “I know this is a really, really difficult time. Your soldiers, your citizens, particularly in the north-east in Kharkiv, are suffering tremendously,” Blinken said. “But they need to know, you need to know, the United States is with you, so much of the world is with you. And they’re fighting not just for a free Ukraine but for the free world, and the free world is with you too.” Blinken is in Ukraine as Moscow’s forces have sought to build on the advantage it has been pressing against depleted Ukrainian forces whose supply of US arms dried up over the winter because of delays forced by Republicans in Congress. Vovchansk – 3 miles from the Russian border and 31 miles from the city of Kharkiv – has been the focus of much of the recent fighting with Ukrainian and Russian troops battling in its streets on Wednesday. Dmytro Lazutkin, the spokesperson for the defence ministry, said “some” Russian infantry groups had entered the town, which military analysts believe Moscow needs to capture to continue its offensive thrust in that direction. Police remained in Vovchansk and were continuing to evacuate people. Nearly 8,000 people have been evacuated from Vovchansk and border areas since Friday’s assault. The capture of the town would be Russia’s most significant gain since it launched an incursion into the Kharkiv region on Friday, opening a new front and forcing Kyiv to rush in reinforcements. “Units of the north group of troops liberated the settlements of Glyboke and Lukyantsi in Kharkiv region and also advanced deep into the enemy defences,” the Russian defence ministry said, announcing its latest gains. The defence ministry also said it had captured the southern Ukrainian village of Robotyne, one of only a handful of settlements Kyiv retook at a huge cost in its summer counteroffensive last year. Ukraine denied the claim as disinformation. Russia is opening new fronts in order to stretch Ukraine’s army, which is short of ammunition and manpower, along the approximately 620 miles (1,000-km) frontline, hoping defences will crumble. Russian artillery and sabotage raids have also been menacing Ukraine’s northern Chernihiv and Sumy regions. The pace of Russia’s advance in the Kharkiv border region, where it launched an offensive late last week and has made significant progress, has slowed, the Institute for the Study of War said late on Tuesday. The Washington-based thinktank said Moscow’s main aim there was to create a “buffer zone” that would prevent Ukrainian cross-border strikes on Russia’s Belgorod region.