"We're confident that Ukraine can, in fact, be a thriving, vital democracy that has strong relationships with Europe and has strong relationships with Russia," Obama said after his first face-to-face meeting with Ukraine President-elect Petro Poroshenko.
"But," Obama added. "that can only happen if we stand clearly behind them during this difficult time."
Obama also announced an increase in non-lethal aid to Ukraine's military, a package that ranges from training to body armor, night vision goggles and other equipment.
A White House report released Wednesday said that the Obama "has approved more than $23 million in additional defensive security assistance since early March."
So far, the administration has resisted calls to send weapons to Ukraine.
In previewing his meeting with Poroshenko, Obama said Tuesday that, "during this crisis, we have provided them nonlethal assistance that's been critical for them."
Poroshenko, who spoke in English, thanked Obama and the U.S. for "continuous" support, which he called "crucially important."
The U.S. and Ukraine leaders also discussed energy security.
Ukraine receives much of its energy supplies from Russia, which has often wielded its oil and gas sales as diplomatic weapons.
As Ukraine seeks alternate sources of energy, Obama said this week that "they're very concerned about making sure that energy is in place as winter comes up."
Poroshenko won the presidency last month in Ukraine's first election since the overthrow of a pro-Russian government earlier this year.
In apparent response, Russia annexed the Crimea region of Ukraine, and President Vladimir Putin vowed to protect the interests of ethnic Russians in Ukraine.
Other nations, including the United States, have accused Russia of instigating violence in eastern and southern Ukraine.
After his meeting with Poroshenko, Obama praised Ukraine's voters for rejecting violence and corruption, another reason they should receive the world's help.
"Obviously, Ukraine has gone through a very challenging time," Obama said.
"And what we have seen has been an incredible outpouring of democracy in the face of actions by Russia as well as armed militias in certain portions of the east who violate international law, violate sovereignty, and have spurred great violence."
Obama's trip to Europe, which began Tuesday in Poland, is designed largely to re-assure allies who are worried about Russia's territorial ambitions in light of the Crimea annexation.
The president began the trip by proposing an additional $1 billion in security aid for NATO allies and other European nations, especially those close to Russia.
Ukraine will be also be the topic when Obama travels Wednesday to Brussels for a Group of Seven summit.
The United States and allies have hit Russia with sanctions, and Obama said more will be forthcoming if Russian President Vladimir Putin continues to encourage divisions in his neighboring nation.
Obama said Putin must recognize and respect Poroshenko's new government if Russia is to rebuild trust with the west.
Obama and Poroshenko are both in Warsaw to celebrate the 25th anniversary of free elections in Poland.
Poroshenko, who will be sworn in as Ukraine's new president on Saturday, also met with U.S. Secretary of State John Kerry, who said the new leader deserves U.S. support.
"He won everywhere, and clearly has been given a mandate to try to lead the country into a new era," Kerry said.
Obama also praised Poroshenko, a candy manufacturer known in Ukraine as "the chocolate king," saying her understands the aspiration of his constituents.
"I have been deeply impressed by his vision," Obama said, "partly because of his experience as a businessman."
Source: USA Today