Shree Chauhan, 33, an education activist who works for an NGO, said she saw Sean Spicer in an Apple shop in Washington DC. Normally, she said, she did not approach public figures, but felt obliged to do so because she was so angry about Mr Trump’s actions.
But she said she was staggered by Mr Spicer’s response. He told her: “It's such a great country that allows you to be here.”
Ms Chauhan, who recorded the encounter on video and posted it online, said she had not initially been aware of what Mr Spicer had said, or the threat she said it implied.
“I watched the video over and over again. I had other people watch it. I watched it with the sound off so I could watch Mr. Spicer’s lips and make sure words match up with the consonants I thought I heard. I watched it with the volume all the way up with my eyes closed,” she said.
“And his words were clear - ‘Such a great country that allows you to be here’.”
She added: “That is racism and it is an implied threat. Think about the sheer audacity of Mr Spicer to say that to my face with a smile, knowing that he that he is being recorded on video and the position of power he holds in our government.”
Ms Chauhan has been attacked on social media for approaching Mr Spicer, and had been quick to defend herself.
In her Medium post, she wrote: “I am still stunned by the boldness of having my citizenship threatened on camera.
“I was not polite. But when does being impolite mean that I should be thrown out of the United States of America? The country I was born in, the country I was raised in, the country I love despite its flaws.”
The video footage showed Ms Spicer initially smiling at Ms Chauhan and ignoring her as she asks about Mr Trump’s alleged links to Russia. He then says: “We have a great country.”
As she persists with her questioning, he adds: “Such a great country that allows you to be here.”
Ms Chauhan wrote: “As someone that has lived in Washington DC for nearly a decade, it is customary to give public figures their space. I’ve left Supreme Court Justice Sonia Sotomayor alone at a grocery store and have done the same for Senator Chuck Grassley on a train.
“However, given what Mr Spicer and his boss are doing to this country, I do not believe they are entitled to these norms and customs.”
The White House has yet to comment on the incident.