Europe has been reluctant to impose tough sanctions due to its reliance on Russian gas and trade ties with Moscow.
But the G7 leaders warned that "we continue to prepare to move to broader, coordinated sanctions, including sectoral measures, should circumstances warrant."
Obama spoke to four European leaders on Friday night about new sanctions against Russia, stressing the need to move quickly, Rhodes told reporters aboard Air Force One.
"Everybody understood that if Russian troops on the border invade Ukraine then sector sanctions will be a response. We need to have a spectrum of sanctions we can impose," said Rhodes.
"We understand that there is unease about the economic consequences of increased sanctions on a large economy like Russia. Our response is that the long-term consequences of allowing Russia to engage in this type of destabilising activity is going to carry its own type of economic costs."
Ukrainian forces move to oust seperatists
Ukraine sent in troops to try to dislodge the separatists for the first time on Thursday, killing up to five rebels around Slaviansk in what it said was a response to the kidnapping and torture of a politician found dead on Saturday.
Russia's foreign minister, Sergei Lavrov, accused authorities in Kiev of waging "war on their own people."
"This is a bloody crime, and those who pushed the army to do that will pay, I am sure, and will face justice," Lavrov said.
The Kremlin says it has the right to defend Russian speakers anywhere if they are under threat and has deployed extra troops on the border with Ukraine, which NATO says number up to 40,000.
They began military exercises on Thursday and Ukraine said they had approached to within 1 km (0.6 mile) of its border and that it would treat any incursion as an invasion.
Ukrainian special forces launched a second phase of their operation on Friday by mounting a full blockade of Slaviansk, the rebels' military stronghold, a presidential official said.
One of its military helicopters was hit by rocket fire and exploded while on the ground at an airport near the city, the Defence Ministry said.
Pro-Western leaders in Kiev, who took power in February after Moscow-ally President Viktor Yanukovich fled following mass protests against him, say they fear Russia will try to take over eastern Ukraine.
Russian troops seized Ukraine's Crimean peninsula on the Black Sea soon after Yanukovich left for Russia in February. Moscow denies interfering in eastern Ukraine, as it did in Crimea before admitting its forces had gone in.