Obama added of the consequences: "And that includes making sure the Ukrainian military does not step into what should be a set of issues that can be resolved by civilians."
It's not the first time Obama has referenced a "line" when it comes to civil unrest in a foreign country. Obama infamously set the so-called "red line" in Syria, but once the Syrian government crossed that line, Obama found little support in Congress for military action.
Update 5:22 p.m.: A number of senators are now calling for sanctions.
Here's Obama's full statement, delivered in Toluca, Mexico, alongside Mexican President Enrique Pena-Nieto:
"The United States condemns in the strongest terms the violence that’s taking place. And we have been deeply engaged with our European partners as well as the Ukrainian government and the opposition to try to ensure that that violence ends. But 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. And I want to be very clear as we work through these next several days in Ukraine that we’re going to be watching closely and we expect the Ukrainian government to show restraint, to not resort to violence in dealing with peaceful protestors. We’ve also said we expect peaceful protestors to remain peaceful and we’ll be monitoring very closely the situation, recognizing that with our European partners and the international community there will be consequences if people step over the line. And that includes making sure the Ukrainian military does not step into what should be a set of issues that can be resolved by civilians. So the United States will continue to engage with all sides in the dispute in Ukraine and ultimately our interest is to make sure the Ukrainian people can express their own desires and we believe 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. But regardless of how the Ukrainian people determine their own future it is important the people themseves make those decisions and that’s what the United States will continue to strive to achieve."
Updated at 2:45 p.m.