Moscow denies sending troops into eastern Ukraine to support pro-Russian rebels battling Ukrainian forces.
Many residents of the Black Sea port are staying put, despite signs that it may soon be the next front in the Ukrainian conflict.
EU had earlier said that new sanctions, targeting Russia's defense and oil companies, could be announced if the cease-fire fell through.
"In some ways, we are solving a non-existent problem because we can't solve the existing ones," a Western defense official, speaking on condition of anonymity, said as the 28-nation summit ended on Friday.
Witnesses saw plumes of black smoke filling the sky on Sunday morning, in a further test for a cease-fire that is barely 40 hours old.
The Ukrainian military and the Kiev authorities have denied the claims, saying that there has been no fighting in the region.
NATO sought to reaffirm its relevancy in a post-Cold War at its Wales summit.
Pro-Russian separatists in Ukraine said on Friday a cease-fire agreement with Ukraine had been reached. The stand-down starts immediately.
Negotiators for Ukraine and pro-Russian rebels are near a cease-fire in Minsk, Belarus, but not much has changed.
The Ukrainian military is reportedly preparing for an imminent rebel attack before a potential cease-fire starting Friday at 7 a.m. EDT.
Rebel forces appear to be making a final push prior to a cease-fire agreement set to take effect on Friday afternoon.
Rasmussen's comments stepped up Western rhetoric against Moscow and set the tone for the two-day meeting.
Weeks after the breach was discovered, investigators have traced the re-routed data to a Russian city, according to a Bloomberg report.
Sergei Lavrov also urged Kiev and pro-Russian rebels in eastern Ukraine to back peace moves outlined by President Vladimir Putin.
On a flight to Mongolia, Putin sketched out a "plan of actions" for peace in Ukraine. The plan will be discussed on Friday at a Belarus summit.
European Energy Commissioner Guenther Oettinger spoke to fears that Russia could cut off Europe's natural gas supplies in the winter.
David Cameron warned that Vladimir Putin must be stopped from seizing Ukraine — a situation that could lead to a new world war.
Ukraine's Poroshenko had earlier claimed in a tweet that a cease-fire was reached in a part of eastern Ukraine, but Russia refuted the claim.
Australia, which will host a G20 summit in November, has said that opposition to Vladimir Putin's presence at the meeting is growing.
Russia denies its troops are involved in fighting on the ground, in the face of what Western countries and Ukraine say is overwhelming evidence.
Vladimir Putin's claims that he could take Kiev in two weeks have been taken out of context, says the Russian president's advisers.
NATO had, on Monday, announced plans to form a "very high readiness force" to respond to Russian aggression in Ukraine.