The United Nations says more than 120,000 people have fled Ukraine.
The civilians are reportedly seeking protection in Poland and other neighboring countries.
Foreign media have reported that there are 15 km long queues near some borders in Ukraine to leave the country.
The majority are women and children.
However, the Ukrainian government has ordered that men between the ages of 18 and 60 be allowed to stay in the country for military purposes.
Foreign media reported that the capital, Kiev, is constantly sounding the siren of missile strikes.
Attacks on the capital, Kiev, have intensified over the past few hours.
The European Commission, France, Germany, Italy, the United Kingdom and Canada, as well as the United States, have issued a joint statement saying Russia has expelled high security Swift Banks from its network of financial institutions around the world.
