Ukraine protests
EU, Ukraine leaders meet as shelling worsens
One serviceman from Ukraine's government forces had been killed and three others wounded.
The threats came in statements issued after a video conference that brought together Obama and world leaders.
Over 5,000 lives have so far been claimed in the conflict.
Fighting in eastern Ukraine is at its worst level since a ceasefire was agreed last September.
Russia has amassed around 20,000 combat-ready troops on Ukraine's eastern border.
The rebel forces said five of their fighters had been killed in the battle for Mariupol.
Plans include further training that will keep about 100 US elite troops on the ground.
Kiev said it had reached a mutual understanding with Moscow on parts of a plan for ending violence.
The Ukrainian army rolled out an offensive against pro-Russia separatists holding the city of Slaviansk.
Kiev has been conducting its anti-terrorist operation in the east of the country since April.
Calm has been restored to Donetsk after violent clashes following the election of Petro Poroshenko.
Petro Poroshenko rejected talks with 'terrorists' & moved towards a military campaign in the east.
Kiev says Moscow must take concrete steps, including withdrawing its troops from the country.
The acting president says a 'yes' vote in tomorrow's referendum would be courting catastrophe.
Ukraine said the Odessa force would replace local police who had failed to tackle rebel actions.
Ukrainian forces launched an operation to retake the eastern town of Slaviansk on Thursday.
Sergei Lavrov said Moscow would respond if its interests, or the interests of Russian citizens, were attacked.
At least three people were killed in a gunfight during the early hours of Sunday.
Russian state television says the people were killed when gunmen attacked a pro-Russian checkpoint.