The Jan. 30-31 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."
In the Reuters/Ipsos poll some 31 percent of people said the ban made them feel "more safe," while 26 percent said it made them feel "less safe." Another 33 percent 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 Republican lawmakers criticized Trump's order and said it could backfire by giving terrorist organizations 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 Reuters/Ipsos poll found that 49 percent of Americans agreed with the order and 41 percent disagreed. Some 53 percent of Democrats said they "strongly disagree" with Trump's action while 51 percent of Republicans said they "strongly agree."
The Reuters/Ipsos poll was conducted online in English in all 50 states. It gathered poll responses from 1,201 people including 453 Democrats and 478 Republicans. It has a credibility interval, a measure of accuracy, of 3 percentage points for the entire sample and 5 percentage points for the Democrats and the Republicans.