One in five Americans believe 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 number who believe he was not born in the US, a constitutional requirement for presidents.

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

White House spokesman Bill Burton said: "The president is obviously a Christian. He prays everyday."

As Obama left to go on holiday, Burton told reporters aboard Air Force One that most Americans care more about the economy and wars in Iraq and Afghanistan and "they are not reading a lot of news about what religion the president is."

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.

"There are two things going on," said Pew's Alan Cooperman. "One is the percentage of people who think Obama is a Muslim is rising and some of that, it is fair to surmise, is an indication of dislike and distrust of the president. But the other thing is that the percentage of Americans who say he is a Christian is dropping and the number who don't know is rising. Those things are true not just among people who don't like the president."

The White House blamed "misinformation campaigns" and "folks who are intent on spreading falsehoods about the president and his values and beliefs".

Conspiracy theories about Obama's faith have dogged him since his presidential campaign, in part fuelled by his middle name – Hussein – and because he attended a school in Indonesia, the world's most populous Islamic country. The questioning has been driven in part by the rightwing media, particularly Fox News, and by bloggers and an internet campaign.

Cooperman said he suspected that a number of those surveyed who said the president was a Muslim do not believe it and were using it as a means to express their dislike of him. A Time magazine poll shows that one in four believe that Muslim citizens are not patriotic Americans. The same poll revealed that an even higher proportion say Muslims should not be permitted to sit on the supreme court or become president.

Cooperman said calling Obama a Muslim was a way of saying that "he's other, he's not one of us".

"For some of them it's a way of registering their distrust to say he's a Muslim because he's repeatedly said he's a Christian after all," said Cooperman.

However, the rising doubts among less hostile sections of the population may be driven by the fact that Obama has not worn his religion on his sleeve. He has not adopted a church in Washington and is not seen to regularly attend church services.

"It so happens that Barack Obama follows eight years in which the previous president was very public and high-profile about his religious beliefs and practices. Following that, Obama is far less high-profile. That may be part of the confusion," said Cooperman. "In the relative paucity of information from the White House and the president himself about religious beliefs, it may be that messages from his critics have gained more currency."