Saudi Arabia's Prince Alwaleed bin Talal has called Donald Trump a disgrace to the US, the latest response to the Republican presidential hopeful's proposed ban on Muslims entering the US.

The Saudi billionaire, a nephew of Saudi Arabia's King Salman, tweeted that Trump should pull out of the US presidential race.

Trump, who still has a commanding lead over other candidates in the Republican race for the White House, tweeted his response.

He called the prince "dopey", accusing him of wanting to "control our US politicians".

Trump's comments have already cost him business in the Middle East, with a major chain of department stores halting sales of his glitzy "Trump Home" line of lamps, mirrors and jewellery boxes.

In Dubai, a $6 billion golf complex stripped Trump's name and image from the site.