Obama announced the sanctions during a news conference in the Philippines, his final stop on a four-country Asia swing.
Ukrainian forces killed up to five pro-Moscow separatists in the east of the country on Thursday.
Ukraine said the drive to root the separatists out would continue and warned it could take "more concrete actions" next week if they do not back down.
Enacting the agreement on the ground though will be difficult, because of the deep mistrust between the pro-Russian groups and the Western-backed government in Kiev
A crowd of around 300 men armed with Molotov cocktails attacked the base, in the south-east part of the country late Wednesday, Interior Minister Arsen Avakov said in a statement.
Tensions continued to mount ahead of high-level diplomatic talks on the Ukraine crisis in Geneva on Thursday after Kiev sent in troops to oust pro-Moscow separatists from the east.
The government in Kiev has struggled to reign in the rebels, as some security forces have switched over to the side of the insurgents.
Putin told German Chancellor Angela Merkel in a telephone call late on Tuesday that Kiev had "embarked on an anti-constitutional course" by using the army against the rebels.
The insurgents, many of them armed, continued occupying government, police and other administrative buildings in nearly 10 cities in the country's Russian-speaking east
The request comes from a government that has proved powerless to reign in separatists in the Russian-speaking east of the country, where insurgents have been occupying government offices in cities for the past week.
He blamed the crisis in Ukraine on the government's lack of respect for the citizens' rights and interests of different Ukrainian regions.
Earlier, a spokesman for the general prosecutor said 12 members of the disbanded 'Berkut' force had been detained on suspicion of shooting peaceful participants in the protests.
Russia annexed Crimea last month following a hastily called referendum held after Russian troops took control of the region. Ukraine and the West have rejected the move as illegal.
NATO had spotted signs of movement by a very small part of the Russian force overnight but had no indication that it was returning to barracks.
NATO suspended all practical cooperation with Russia on Tuesday in protest at its annexation of Crimea and ordered military planners to draft measures to strengthen its defences.
The US Senate and House of Representatives easily passed bills on Thursday to provide aid to Ukraine, back a $1 billion loan guarantee for the Kiev government and impose sanctions on Russians.
Ukraine's new leaders acted after Monday night's violence in Kiev city centre, conscious that an increasing criminal climate could discredit the anti-Yanukovych uprising
And from folklore to ancestral traditions, Ukraine has shown itself to possess a distinct identity.
The new leadership seemed on edge after a far-right radical group that played a central role in the revolt that overthrew president Viktor Yanukovych rallied angrily outside parliament, demanding the dismissal of interior minister Arsen Avakov.