U.S authorities are investigating an incident in which a pig's head was thrown at a mosque in Philadelphia early on Monday morning, as worries grow over a rise in Islamophobia after a Muslim couple killed 14 people at a holiday party in California.

The Federal Bureau of Investigation is examining the incident, spokeswoman Carrie Adamowski said on Tuesday.

Philadelphia Mayor-elect Jim Kenney decried what he called an act of bigotry. "We cannot allow hate to divide us now, in the face of unprecedented difficulties," he said in a statement.

Surveillance video showed a red truck driving past the Al-Aqsa mosque in North Philadelphia on Sunday night and someone throwing an object from the window, police said. A caretaker discovered the pig's head early on Monday, they said.

American Muslims have expressed concern about an increase in Islamophobia since authorities said a young Muslim couple, Syed Rizwan Farook and Tashfeen Malik, stormed a party attended by San Bernardino County employees on December 2, leaving 14 people dead and 21 wounded.

Republican presidential front-runner Donald Trump called on Monday for a ban on Muslims entering the United States, drawing fierce criticism from both the White House and rivals candidates in his own party.