The next round of sanctions on Russia over the Ukraine crisis could target prominent Russians in the energy and banking industries and could come early next week, a senior White House official said on Saturday.

US Deputy National Security Advisor Ben Rhodes, speaking on Saturday to reporters aboard Air Force One en route to Malaysia with President Barack Obama, said sanctions could target "individuals with influence on the Russian economy, such as energy and banking."

"When you start to get at the cronies, the individuals who frankly control large parts of the Russia economy, and some of the entities under their control, you are imposing a significant economic impact beyond strictly sanctioning an individual," he said.

He did not give a date when the sanctions would be imposed, but said it would not happen over the weekend.

"I would expect ... targeted sanctions would be imposed with urgency" and could come "early next week."

Earlier a US official told AFP that the new round of US sanctions could come as early as Monday.

Rhodes spoke after the Group of Seven rich countries -- Canada, France, Germany, Italy, Japan, the United Kingdom, the United States -- agreed Saturday to impose new sanctions on Russia over the crisis in Ukraine.

The G7 nations, in a joint statement, gave no date but said they would "move swiftly to impose additional sanctions on Russia."

Rhodes spoke of "a spectrum of sanctions" that "allows us to escalate further" if the situation in Ukraine deteriorates further.

Obama on Friday said that new sanctions against Russia were "ready to go" but signaled they would not target key areas of the Russian economy such as mining, energy and the financial sectors.

US officials have said those measures would only be considered if Russia sent its regular forces across the border into eastern Ukraine.

"We understand there is unease about the economic consequences of sanctions on a large economy like Russia ... There is a degree of unease in the private sector," Rhodes said.