Rhodes said that sanctions were the best way to put pressure on Russia, denying a report from the New York Times that US officials had already taken the decision to arm the Kiev government in its fight against pro-Russian separatists.
US President Barack Obama had told his advisors to examine “all the options”, Rhodes said, adding that Washington would prefer to see a peaceful de-escalation of the conflict.
Rhodes' remarks echoed the feeling among members of the German government ahead of a meeting between Obama and Merkel next week.
“I say this to our American friends too, who are considering whether to send weapons – there will be no military solution to this conflict," Foreign Minister Frank-Walter Steinmeier told a Social Democratic Party (SPD) conference in Nuremberg.
“Even in the best case, there will be more deaths. Real political solutions are reached at the negotiating table, never in the muzzle flash of rifles.”
Merkel had earlier ruled out German weapons deliveries to Ukraine during a visit to Hungarian capital Budapest on Monday.
“I'm firmly convinced that this conflict can't be solved militarily,” the Chancellor said.