The authorities issued the tough warnings as foreign ministers held a European security conference in a city seething with unrest over the Ukrainian government's U-turn away from Europe back towards Russia.
Germany's visiting foreign minister used the occasion to warn Ukraine against violently cracking down on protesters.
Russia's responded by accusing EU officials of "hysteria".
Kiev's November 21 decision to abandon a trade and integration deal with the EU and pursue closer economic ties with Moscow brought hundreds of thousands of demonstrators into the streets over the weekend.
Protesters have since blockaded the main government headquarters and occupied Kiev's city hall.
Prime Minister Mykola Azarov defended his government's handling of the crisis.
He clashed sharply with Germany's Foreign Minister Guido Westerwelle, who has used his visit to Kiev for a conference of the Organization for Security and Cooperation in Europe to show solidarity with the demonstrators.
"Nazis, extremists and criminals cannot be, in any way, our partners in 'Eurointegration'," the government website quoted Azarov as telling Westerwelle.
Westerwelle expressed concern about police behavior at the protests, when dozens of people were severely beaten.
"Recent events, in particular the violence against peaceful demonstrators last Saturday in Kiev worry me greatly," said Westerwelle.
"The way Ukraine responds to the pro-European rallies is a yardstick for how seriously Ukraine takes the shared values of the OSCE."
In a pointed gesture, Westerwelle visited the main protest center on Kiev's Independence Square on Wednesday and met opposition leaders who have called for Yanukovich to resign.
Several other EU ministers made the same trip on Thursday.
The crisis has exposed a gulf between Ukrainians, many from the west of the country, who hope to move rapidly into the European mainstream, and those mainly from the east who look to the former Soviet master Moscow as a guarantor of stability.
EU countries, especially those like Germany and Poland with experience of Cold War-era Russian domination, are keen to bind Ukraine and its 46 million people closely with the West and say their trade pact would have brought a surge of investment.
Moscow wants Kiev instead to join a customs union that it dominates with other ex-Soviet republics.
Russia exerts powerful leverage because of Ukraine's dependence on its natural gas.
A court ordered the protesters on Thursday to quit the Kiev mayor's office, where they have set up an operational hub, and halt their four-day blockade of government buildings.
In perhaps the strongest signal yet that the authorities are contemplating action to reclaim the streets, the head of the Kiev police, Valery Mazan, said:
"We do not want to use force. But if the law is broken, we will act decisively, harshly.
"We will not try to talk people round. We have the means and capability laid down by the law," he added.
The stand-off between pro-EU protesters and the government is taking a toll on the fragile economy.
The central bank has twice been forced to support the currency this week and the cost of insuring Ukraine's debt against default has risen further.
Ukraine faces a $17 billion bill next year for debt repayments and deliveries of Russian gas.
About 3,000 pro-Europe demonstrators, mainly from western Ukrainian-speaking parts of the country, have been camped out in Independence Square since Sunday.
They huddle round blazing braziers, swap anecdotes about events of the day and follow news developments on a huge TV screen.
Speaking to the OSCE session, Victoria Nuland, U.S. Assistant Secretary for European and Eurasian Affairs, urged "all sides" to renounce violence, respect the right to peaceful assembly and the rule of law.
Russian Foreign Minister Sergei Lavrov spoke scathingly about Europe's reaction to Ukraine's decision to seek closer trade ties with Moscow.
"This situation is linked with the hysteria that some Europeans have raised over Ukraine which, using its sovereign right, decided at the current moment not to sign any agreement which Ukrainian experts and authorities considered disadvantageous," Russia's Itar-Tass news agency quoted Lavrov as saying on the sidelines of the OSCE meeting.
Yanukovich, who is visiting Beijing, suggested some relief could be on the way for the distressed economy, signing documents for deals with China on agriculture, infrastructure improvement and energy.
He estimated their value at about $8 billion of investment in the Ukrainian economy.
Ukraine faces huge problems in financing its current account deficit.
Severely depleted central bank reserves are also putting Ukraine at risk of a balance-of-payments crunch.
One analyst, Timothy Ash of Standard Bank, doubted the long-term investment commitments from China would help an immediate cash shortage.
"Ukraine needs short term cash/financing, and likely of the order of USD $10-15bn at this stage in up-front cash to make a difference," he said.
TYMOSHENKO CALL FOR SANCTIONS
The Kiev government says it has not ditched the trade deal with Europe but is taking a strategic "pause" while it negotiates a new "roadmap" with Russia to patch up its economy.
Protesters consider the move to have been an abrupt reversal to Ukraine's march towards Europe.
They hope to repeat the success of the "Orange Revolution" nine years ago, when mass demonstrations forced the overturning of a fraudulent presidential election victory for Yanukovich.
Azarov's deputy, Serhiy Arbuzov, who is preparing to head Ukraine's first high-level delegation to Brussels soon to repair some of the political damage, suggested the government might be ready to consider one of the opposition's demands - early parliamentary elections.
There has been no suggestion from Azarov that he is ready to go along with this idea.
Before negotiations were halted, the EU had pressed Ukraine to release Yulia Tymoshenko, who served as prime minister after the Orange Revolution but lost a presidential election in 2010 to Yanukovich and was later jailed for abuse of office.
Brussels considers her a political prisoner.
On the eve of a fresh attempt to bring her to trial on new charges, Tymoshenko called for the West to apply "targeted sanctions" against Yanukovich and his family.
This "is the only language he understands," she said, according to her lawyer.
Source: Yahoo News