The Russian advances appeared to bring the Kremlin closer to taking full control of Luhansk province, one of Moscow's stated war objectives, and set the stage for Lysychansk to become the main frontline city on that front.
Although the approval of the Kyiv government's application by EU leaders meeting in Brussels is just the start of what will be a years-long process, it marks a huge geopolitical shift and will anger Russia as it struggles to impose its will on Ukraine.
The Russian strikes on Kharkiv, throughout Tuesday and continuing on Wednesday morning, were the worst for weeks in the area where normal life had been returning since Ukraine pushed Russian forces back in a major counter-offensive last month.
The latest diplomatic crisis is over the Kaliningrad enclave, a port and surrounding countryside on the Baltic Sea that is home to nearly a million Russians, connected to the rest of Russia by a rail link through EU- and NATO-member Lithuania.
Moscow's separatist proxies claimed to have captured Toshkivka, a town on the mostly Ukrainian-held western bank of the Siverskyi Donets river, south of Sievierodonetsk, which has become the main battlefield city in recent weeks.
Ukraine applied to join the EU just four days after Russian troops poured across its border in February. Four days later, so did Moldova and Georgia — smaller ex-Soviet states also contending with separatist regions occupied by Russian troops.
On the battlefield, Ukrainian officials said their troops were still holding out against massive Russian bombardment in the eastern city of Sievierodonetsk, and described new progress in a counteroffensive in the south.
Russia had told Ukrainian forces holed up in a chemical plant in the shattered city to stop "senseless resistance and lay down arms," pressing its advantage in the battle for control of eastern Ukraine.
In southern Ukraine, another major battleground in the war, authorities said Russian attacks on agricultural sites including warehouses were compounding a global food crisis that has stirred concerns of famine in some developing countries.
The Ukrainian defenders had over the weekend regained control over about half the city just as the Russians appeared on the verge of victory. But their position had again become more perilous on Monday morning.