"Would you also agree that Emma Lazarus's words etched on the Statue of Liberty, 'Give me your exhausted, give me your poor, ' are also a part of the American ethos?" He said Europe had "class based societies where people were considered wretched if they weren't in the right class".
The rule is slated to take effect on October 15 and would apply to public assistance used after that point.
The rule change is meant to reinforce "ideals of self-sufficiency", officials said. Many critics argue this unfairly targets low income migrants.
What did the official say?
This is Cuccinelli speaking to NPR's Rachel Martin. "Once they arrived, my grandfather wanted to make sure his cousins spoke English-certainly well enough to work-and listed my father in that effort, as well, to make sure they could speak English well enough to work".
"The rule is complicated and understanding precisely who will be subjected to this new public charge test is hard for families to discern", said Andrea Kovach, a senior attorney at the Shriver Center on Poverty Law. On Tuesday, Cuccinelli explained to NPR that self-sufficiency has always been expected of immigrants, regardless of what people may think the poem stands for.
"I lift my lamp beside the golden door!"
"In the case of my own family, my Italian grandfather played this role, sponsoring two of his cousins, Mario and Silvio, to come to America", said Cuccinelli.
Mr Cuccinelli later criticised the outcry, telling CNN: "I'm not rewriting poetry". He insisted he was answering a question and accused people on the left of "twisting" his comments. But she said she worries immigrants won't use those much needed services "out of fear and misinformation", even though using them wouldn't adversely affect their immigration applications.
"This administration finally admitted what we've known all along: They think the Statue of Liberty only applies to white people", tweeted former Texas Rep. Beto O'Rourke, a Democratic presidential candidate.
Individuals deemed "public charges" may be denied entry into the United States or denied a green card. This practice would mean that the cost of services would shift from federal to state governments, the counties argued.
Those already in the U.S. could also have their applications rejected.
According to a study by the nonpartisan Migration Policy Institute, the rules would likely reduce immigration from Mexico and Central America, while increasing it from other regions, especially Europe.
The Trump administration's immigration policy was criticized from the beginning of his campaign for President.
The Homeland Security Department did not immediately respond to a request for comment.
About half a million immigrants apply for green cards each year in the U.S. But under new rules, the vast majority could be at risk of being denied permanent legal status. Ferguson joined 18 other attorneys general who expressed concerns in a separate letter.
Cuccinelli was asked earlier Tuesday on NPR whether the words "give me your exhausted, your poor" were part of the American ethos.