Russian forces have stepped up their offensive on cities in eastern Ukraine, as Tuesday marked three months since the start of their invasion of the country.

Russia's defense ministry said on Tuesday that the military used missiles to destroy an ammunition depot and other targets in the Donetsk region. It added that the military shot down a Ukrainian fighter aircraft near Kramatorsk.

Russia aims to capture the entire Donetsk and Luhansk regions. Its forces are believed to have taken control of about 90 percent of Luhansk.

Britain's defense ministry said on Tuesday that "Russia has increased the intensity of its operations in the Donbas as it seeks to encircle Severodonetsk, Lyschansk and Rubizhne."

It also said Ukraine's resistance has been strong, and that the its military "likely retains effective command and control of this front." But it said Russia has "achieved some localized successes, due in part to concentrating artillery units."

The ministry warned that if Russia captures Severodonetsk, the entire Luhansk region will be placed under Russian occupation.

US think tank the Institute for the Study of War reported on Monday that Russian troops were advancing to Severodonetsk from the south, and trying to cut off Ukraine's supply lines in the north.

Ukrainian President Volodymyr Zelenskyy said in a video address released on Monday that the coming weeks will be difficult in the fight against Russia, and that Ukraine has no choice but to fight to free its land and people.

He called on Western and other countries to continue military support for Ukraine.

Russian Security Council Secretary Nikolai Patrushev, a close aide to President Vladimir Putin, told the country's media on Tuesday that Russia will accept a prolonged war. He said the country will achieve all goals set by the president without deadlines.