A survey by the Pew Global Attitudes Project found that an overwhelming 82 percent of French respondents support a ban. The poll found 71 percent support in Germany, 62 percent in Britain and 59 percent in Spain.
In the United States, 28 percent of those questioned said they would approve a ban.
Several European countries have been considering bans on such veils, with special attention on France, home to western Europe's largest Muslim community and a strongly secular government.
The lower house of France's parliament is expected to approve a divisive bill Tuesday that would make it illegal to wear full-face veils in public. The government says such veils oppress women. Only a very small minority of French Muslim women wear veils such as the niqab or burqa, and many French Muslims fear a ban would stigmatize the whole Islamic community.
The pollsters questioned more than 4,000 people by telephone in the five countries as part of a larger poll on global attitudes conducted in April and May. The margin of error was plus or minus 4 or 5 percentage points for the countries asked about the veil. The study was released Thursday.
In the United States and Europe, respondents to the poll who were over 55 were more likely to support a ban than those age 18 to 34.
Those on the political right were more likely to support a ban than those on the left, except in Spain.
The pollsters said there was no variation along gender lines in any of the five countries and little variation depending on income and education levels.
The French government's proposed veil ban is widely expected to become law after Tuesday's lower house vote and a vote in the Senate in September.
The government has insisted that the bill is not about religion but has called it a way to promote equality between the sexes, to protect oppressed women or to ensure security in public places.
While the proposed legislation is colloquially referred to as the "anti-burqa law," it is officially called "the bill to forbid covering one's face in public." Part of the bill is aimed at husbands and fathers who impose such veils on female family members.
Citing security reasons, Belgium's lower house has enacted a ban on the face-covering veil, though it must be ratified by the upper chamber. Calling them an affront to human dignity, Spain's government has said it favors barring the use of burqas in government buildings.
Germany's interior minister, however, has said he sees no need for a debate on whether to ban full-body veils in Germany.