One in five Americans believes Barack Obama is secretly a Muslim and nearly half question his claim to be a Christian, according to a new opinion poll.

The survey by the Washington-based Pew Research Centre reflects a broader questioning among many Americans as to whether Obama is a "real" American – also reflected in the significant numbers of people who believe he was not born in the US, a constitutional requirement to be president.

According to the poll, 18% of Americans say Obama is a Muslim, a steep rise on a similar survey a year ago when the figure was 11%. The number of people who said the president is a Christian dropped to 34% from 43% last year.

Suspicion that Obama is an adherent of Islam is highest among conservative Republicans, a third of whom believe he is a Muslim. But there are doubts even among many of the president's supporters with fewer than half accepting his assurance that he is a Christian.