Lawyers said in court filings submitted on Friday, the Trump administration will continue to pursue a way of adding a citizenship question to the census.
But administration lawyers failed to provide any legal justification for the census question by a court deadline.
The Supreme Court rebuffed the initial rationale for adding the question to the 2020 census as "contrived".
The question is controversial because critics believe it will discourage immigrants from taking part.
They say that lower participation by immigrants could lead to an undercount of populations in Democratic districts, benefiting President Donald Trump's Republican Party and altering how congressional seats are allocated and billions of dollars of federal funds distributed in those districts.