US President Barack Obama has condemned what he called Russia's "dark tactics" and "bullying" in Ukraine, prompting President Vladimir Putin to hit back at American "aggression," as diplomatic wrangling between the two countries escalated.

Obama met Ukraine's president-elect Petro Poroshenko in the Polish capital of Warsaw on Wednesday, and promised years of US support, then blasted Russia and vowed to protect former Soviet states and domains in NATO, in a speech marking Poland's 25 years of democracy.

"How can we allow the dark tactics of the 20th century to define this new century?" Obama asked.

In a clear reference to Russia's annexation of Crimea and its actions in wider Ukraine, Obama warned that "the days of empires and spheres of influence are over.

"Bigger nations must not be allowed to bully the small, or impose their will at the barrel of a gun or with masked men taking over buildings.

"So we will not accept Russia's occupation of Crimea or its violations of Ukraine's sovereignty," Obama said, before he left for Belgium and a G7 summit dedicated to coordinating policy towards Moscow.

During his visit to Poland, Obama also proposed a $1bn fund to finance new US air, naval and troop rotations through Eastern Europe, launching his regional tour designed to bolster NATO resolve and capacity against Moscow.

Face-to-face in Normandy

Obama will come face-to-face with Putin on Friday in France. Several European leaders are also meeting the Russian leader and hope to pursue dialogue to ease the Ukraine crisis.

Putin said that he could not understand why Obama, who has spent months trying to isolate him over Ukraine, would not hold a formal meeting with him during 70th anniversary commemorations in Normandy.

"It is his choice, I am ready for dialogue," Putin said in an interview with French broadcasters Europe1 and TF1 conducted at his dacha in the Black Sea resort of Sochi.

The Russian leader accused the US of hypocrisy in its "aggressive" attempts to punish Russia over Ukraine.

"We have almost no military forces abroad yet look: Everywhere in the world there are American military bases, American troops thousands of kilometres from their borders."

Clashes continue

Meanwhile, in eastern Ukraine, three government soldiers were injured in a massive all-night attack carried out by hundreds of pro-Russian fighters, authorities in Kiev said.

The assault on a position held by the Ukrainian National Guard in the Luhansk region began Tuesday evening and lasted 10 hours, the Interior Ministry said, adding that six rebels were also killed in the fighting.

The 300 rebels who took part in the attack were armed with automatic weapons, rocket launchers and mortars, and the Ukrainian forces fought "to the last bullet," according to the ministry.

Also on Wednesday, Al Jazeera's Kim Vinnell, reporting from Ukraine's Donetsk city, said that heavy fighting had resumed in Slovyansk.

"Heavy fighting resumed this morning in Slovyansk, which has been a hotspot thoughout this conflict. It is a very dangerous situation for the civilians in the city," she said.

"Pretty much the whole town is cut off. There are block posts manned by armed pro-Russia separatists. They said all of the roads leading into Slovyansk had [Ukrainian government] snipers looking down on them."

Washington has accused Moscow of coordinating and directing the rebels, and said continued fighting should merit tough new economic sanctions.