(CNN) A huge majority of Americans want there to be a way for immigrants living in the US illegally to stay in the country legally, if requirements are met, according to a new survey by the Pew Research Center out Monday.

Over the last week, immigration authorities rounded up 680 undocumented immigrants in a record-setting operation, taking place at seven sites in six cities in Mississippi . The raids are believed to be the "the largest single-state immigration enforcement operation in our nation's history," according to US Attorney for the Southern District of Mississippi Mike Hurst.

The survey was conducted from late July to early August, before the raids in Mississippi, and found 72% of Americans want there to be a path to legal status for undocumented immigrants, while only about a quarter think there should be a national law enforcement effort to deport all undocumented immigrants.

Republicans and Republican-leaning independents mostly agree that there should be a legal way for undocumented immigrants to remain in the US (54%), but that view is on the decline, down 5 percentage points since a March 2017 Pew poll. Almost 9 in 10 Democrats and Democratic-leaning independents support a legal way for undocumented immigrants to become citizens, which is steady since 2017.

Republicans are also more apt to back a national law enforcement effort to deport all undocumented immigrants in the US -- 42% of all Republicans and Republican-leaning independents and almost half (49%) of conservative Republicans.

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