"Sham referenda and mobilisation are signs of weakness, of Russian failure," Bridget Brink wrote in a Twitter message.
"The United States will never recognise Russia's claim to purportedly annexed Ukrainian territory, and we will continue to stand with Ukraine for as long as it takes," she said.
Putin ordered a partial military mobilisation earlier on Wednesday and vowed to use "all available means" to protect Russian territory, after Moscow-held regions of Ukraine suddenly announced annexation referendums.
Ukrainian President Volodymyr Zelenskyy's advisor Mykhaylo Podolyak mocked Moscow's latest steps in a Twitter message.
"Everything is still according to the plan, right? Life has a great sense of humour," he wrote.
"210th day of the 'three-day war'. Russians who demanded the destruction of Ukraine ended up getting: 1. Mobilisation 2. Closed borders, blocking of bank accounts 3. Prison for desertion," said Podolyak.
On Tuesday separatist officials in Moscow-held regions of Ukraine announced urgent votes on annexation by Russia.
Pro-Russia authorities in the eastern Donetsk and Luhansk regions, as well as in the southern Kherson and Zaporizhzhia regions, said they would hold the vote over five days beginning on Friday this week.
Washington, Berlin and Paris denounced the ballots and said the international community would never recognise the results while NATO said the votes marked a "further escalation" of the war.
Putin "still refuses to understand Ukraine", said the UK's ambassador in Kyiv.
"Partial mobilisation and sham referenda don't change that essential weakness," Melinda Simmons wrote on Twitter.