At least 26 people were killed in clashes between protesters and police on Tuesday, triggering international condemnation. (Agencies)
The Foreign Ministers of Germany, France and Poland are heading to Ukraine to meet its President on Thursday.
"We hold the Ukrainian government primarily responsible for making sure that it is dealing with peaceful protesters in an appropriate way, that the Ukrainian people are able to assemble and speak freely about their interests without fear of repression," Obama said during a visit to Mexico.
"I want to be very clear that as we work through these next several days in Ukraine that we are going to be watching very carefully and we expect the Ukrainian government to show restraint, to not resort to violence in dealing with peaceful protesters," he said.
Obama said the United States also expected the protesters to remain peaceful.
"We will be monitoring very carefully the situation, recognising, along with our European partners and the international community, there will be consequences if people step over the line," he said.
This includes making sure that the Ukrainian military does not step into what should be a set of issues that can be resolved by civilians, the US President said.
He said he believes that a large majority of Ukrainians are interested in an integration with Europe, and the commerce and cultural exchanges that are possible for them to expand opportunity and prosperity.
Soon after the warning by Obama, the United States imposed visa travel bans on 20 senior members of the Ukrainian government.
The US and the EU are considering imposing sanctions on Ukraine, a senior State Department official said.
In view of the truce agreement between Ukrainian president and protest leaders, a senior State Department official told reporters on condition of anonymity that there was some glimmer of hope in this country.
"There are announcements coming out of both the opposition and the government that as a result of the president's meeting tonight with the three opposition leaders, Arseniy Yatsenyuk, Vitali Klitschko and Oleh Tyahnybok, that there is now a truce been called to allow for negotiations to restart aimed at ending the bloodshed and stabilising the situation," the official said.
At least 26 people were killed in clashes between protesters and police on Tuesday, triggering international condemnation.