Olga Stefanishyna told the BBC that, after "strong resistance" from the Ukrainian army, there was an "enormous operation" by Russia against civilians.
On Sunday alone, a family of four were killed when Russians fired shells at people fleeing the conflict in Irwin.
And in the port city of Mariupol, a mass evacuation had to be called off.
The city is now in its fifth day with no running water, no power, no sanitation, and food and water are fast running out.
However, the city council there said plans to get civilians to safety had been aborted for the second day running because Russian shelling had made it impossible. Russia has blamed Ukrainian forces.
The World Health Organization also said health facilities were being attacked, with its director-general saying they had caused "multiple deaths and injuries".
The British government has accused Russia of targeting populated areas "in multiple locations", noting in an intelligence update. That it had "previously used similar tactics in Chechnya in 1999 and Syria in 2016".
On Sunday, UN monitors said 364 civilian deaths had been confirmed in Ukraine since the invasion began on 24 February, but the real figure was likely to be "considerably higher".
The UNHCR said more than 1.5 million people had fled Ukraine since Russia invaded.
But Russia denies targeting civilians, saying it is carrying out a "special military operation" against Ukrainian "nationalists" and "neo-Nazis".
Ms Stefanishyna - who was speaking to BBC TV's Sunday Morning program - accused Russia of "military tactics right in the cities of Ukraine", adding they were carrying out a "terroristic plan", with attacks coming from the air and also by land.
" The Shelled hospitals, the shelled houses for kindergartens and schools, and the ordinary households," she said. "This is how the reality looks."
She said Ukraine was seeing "another wave of implementation of this terroristic plan of [the] Russian Federation".
Ms Stefanishyna claimed Russia was suffering "enormous losses" of soldiers and equipment, but this "does not deter Russia".
"It only encourages further aggression," she said.
The family's deaths in Irwin, north-west of Kyiv, happened when Russian mortar shells targeted a damaged bridge that people were using in an effort to escape the violence.
Attacking civilians and civilian infrastructure - such as schools and hospitals - is against the Geneva Conventions, which are treaties agreed by all countries that are supposed to regulate war.
As well as the WHO, other non-government organizations have also reported attacks on civilian targets.
Amnesty International says it has verified various attacks - including cluster munitions hitting a kindergarten and nursery, and a ballistic missile hitting a hospital.
Finland ought theoretically to be safe, since it has historically been neutral and gave Stalin's Soviet army a hard time when he invaded the country in 1939.
There has never been much support here to join the NATO military alliance. But when the spokeswoman for the Russian foreign ministry recently warned Finland and Sweden explicitly that any move towards NATO could have military consequences, people in both countries were deeply shocked.
Since then, Russian warplanes have blatantly intruded into Swedish airspace.
If being neutral is not sufficient to guard against Russia, people here are saying that maybe joining NATO will give the two countries the protection they need.
This represents a major change of mood. In Finland, particularly, relations with Russia were thought to be pretty good.
The Ukraine invasion has changed everything.
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