Blasts were heard before dawn on Monday in the capital of Kyiv, breaking a few hours of quiet, and in the major city of Kharkiv, Ukraine's State Service of Special Communications and Information Protection said.
The Ukrainian military said it struck Russian convoys heading towards the city while a military spokesperson said the Russians had been attacking from numerous fronts.
According to Russian news agencies, talks between Russia and Ukraine are due to begin in Belarus later on Monday in efforts to end the fighting.
The Washington post on Monday, quoted a U.S. official who said that Belarus was preparing to join the Russian invasion force.
Ukrainian President Volodymyr Zelensky said he was not optimistic that the talks would yield results but was prepared to give them a chance so that the people of Ukraine know that all efforts to end the war, are made.
Zelensky told British Prime Minister Boris Johnson in a phone conversation on Sunday, that the next 24 hours would be crucial for Ukraine, a Downing Street spokesperson said.
On Sunday, satellite pictures revealed a 5 kilometer (3.1 mile) long Russian convoy heading towards Kyiv. The convoy included armed personnel carriers, tanks and fuel trucks.
So far, the Russian offensive cannot claim any major victories. Russian has not taken any Ukrainian city, does not control Ukraine's airspace, and its troops remained roughly 30 km (19 miles) from Kyiv's city center the official said.
Russia calls its actions in Ukraine a "special operation" that it says is not designed to occupy territory but to destroy its southern neighbor's military capabilities and capture what it regards as dangerous nationalists.
As sanctions against Russia increase, South Korea said it will tighten export controls against Russia, by banning exports of strategic items, and join Western countries' moves to block some Russian banks from the SWIFT international payments system, Seoul's foreign ministry said on Monday.
The Korean government has also decided to promote the additional release of strategic oil reserves for stabilization of the international energy market and to further review other measures such as the resale of LNG to Europe, the ministry said in statement.
Singapore intends to impose "appropriate sanctions and restrictions" on Russia, the city-state's foreign minister Vivian Balakrishnan told parliament on Monday, the Straits Times newspaper reported.
Japan also said it is working closely with G7 nations to ensure effective economic sanctions against Russia and its central bank, its top currency diplomat said after a meeting of government and central bank executives to debate the fallout from the Ukraine crisis.
"We will respond, working closely with the international community including the G7 nations, so that we exert maximum cost to Russia" for invading Ukraine, Masato Kanda, vice finance minister for international affairs, told reporters on Monday.
The Russian ruble tumbled to a record low against the dollar on Monday, and Russia's central bank announced a slew of measures to support domestic markets, as it scrambled to manage the broadening fallout of harsh Western sanctions.
The central bank said it would resume buying gold on the domestic market, launch a repurchase auction with no limits and ease restrictions on banks' open foreign currency positions.