Leading American senators have called for the US to send weapons to help Ukraine fight what they say is "a Russian invasion".
Robert Menendez, head of the Senate Foreign Relations Committee, said Russia's President Vladimir Putin must face a cost for his "aggression".
Senator John McCain said: "This is not an incursion. This is an invasion."
Earlier, Putin called for talks to discuss the matter of "statehood" for eastern Ukraine.
The conflict in eastern Ukraine erupted in April following Russia's annexation of Ukraine's southern Crimea peninsula a month before. Some 2,600 people have died since April.
Pro-Russian separatists have been gaining ground on Ukrainian forces in recent days, in both the Luhansk and Donetsk regions, and further south around the port of Mariupol.
Speaking on CNN, Menendez, a Democrat, said: "We should provide the Ukrainians with the type of defensive weapons that will impose a cost upon Putin for further aggression.
"This is no longer the question of some rebel separatists, this is a direct invasion by Russia. We must recognise it as that."
He said the issue "may very well be on the table right now" for President Barack Obama.
Senator McCain told CBS's Face the Nation that Putin was "an old KGB colonel that wants to restore the Russian empire".
McCain called for "strong sanctions", before adding that Ukraine must be supplied with weapons: "Give them the weapons they need. Give them the wherewithal they need. Give them the ability to fight."
Representative Mike Rogers, chairman of the House Intelligence Committee, told Fox News: "If we don't provide 'small and effective' now, you're going to get very big and very ugly later."
In Ukraine, there were reports of a first naval encounter in the conflict.
Pro-Russian separatists fired artillery shells at a Ukrainian patrol vessel in the Azov Sea, with the Ukrainian military saying a rescue operation was under way.
The rebels have gained ground in the far south-east, pushing towards Mariupol, where Ukrainian troops and local residents are strengthening defences.
But many have fled the city of 500,000 people.
Ukraine and the West blame Russian military support for the recent rebel gains, saying armoured columns have crossed the border. Russia denies military involvement.
Earlier, Putin said the issue of "statehood" for eastern Ukraine needed to be discussed to ensure the interests of local people were "definitely upheld".
"Russia cannot stand aside when people are being shot at almost at point blank," he said, describing the rebels' actions as "the natural reaction of people who are defending their rights".
The West, Putin said, should have foreseen Russia's reaction to the situation, adding it was impossible to predict how the crisis would end.
Putin's spokesman, Dmitry Peskov, later said the president's remarks on "statehood" should not be taken to mean an actual separate entity, and that the Ukrainian crisis was a "domestic" one.
Putin's comments came after the EU gave Russia a one-week ultimatum to reverse course in Ukraine or face more sanctions.
Putin dismissed the EU threat, accusing it of "backing a coup d'etat" in Ukraine.
The EU and US have already imposed asset freezes and travel bans on many senior Russian officials and separatist leaders in eastern Ukraine.
On Saturday, Ukrainian President Petro Poroshenko said: "I think that we are very close to the point of no return. Point of no return is full-scale war."