Imposing a temporary travel ban on citizens from seven Muslim countries, President Donald Trump said the move would help protect the United States from terrorism.
But less than one-third of Americans believe the move makes them "more safe", according to a new poll.
The January 30-31 Reuters/Ipsos poll found roughly one in two Americans backed the ban, which also suspends admission of all refugees for 120 days, although there were sharp divisions along party lines.
Trump has pushed back against critics who say the travel ban targets Muslims. He says the "extreme vetting" is necessary to protect the country and its borders.
"This is not about religion," Trump said in a statement after announcing the travel ban on Friday. "This is about terror and keeping our country safe."
About 31 per cent of those polled said the ban made them feel "more safe," while 26 per cent said it made them feel "less safe".
Another 33 per cent said it would not make any difference and the rest said they don't know.
Trump's executive order blocked citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen and placed an indefinite ban on Syrian refugees.
Some Republicans criticised Trump's order and said it could backfire by giving terrorist organisations a new recruitment message.
"This executive order sends a signal, intended or not, that America does not want Muslims coming into our country," senators John McCain of Arizona and Lindsey Graham of South Carolina said in a joint statement.
The poll found 49 per cent of Americans agreed with the order and 41 per cent disagreed. About 53 per cent of Democrats said they "strongly disagree" with Trump's action while 51 per cent of Republicans said they "strongly agree".
Democrats were more than three times as likely as Republicans to say the "US should continue to take in immigrants and refugees" and Republicans were more than three times as likely as Democrats to agree that "banning people from Muslim countries is necessary to prevent terrorism".
The poll was conducted online in English in all 50 states. It gathered poll responses from 1201 people including 453 Democrats and 478 Republicans.