Presidential candidates Donald Trump and Hillary Clinton adjusted their presidential politicking on Sunday, offering prayers and support to the victims. But then they infused their sympathy with sharply different statements that favor their White House aspirations, and the presidential race rolled on.

Clinton pushed for gun control and reached out to gays and lesbians, a key constituency.

"The gunman attacked an LGBT nightclub during Pride Month. To the LGBT community: please know that you have millions of allies across our country. I am one of them," she said, adding a call to keep assault weapons out of the hands of "terrorists or other violent criminals".

Trump also offered words of support. On Twitter, he renewed talk of his plan to ban Muslims from the US for an indeterminate time.

"Is President (Barack) Obama going to finally mention the words radical Islamic terrorism? If he doesn't he should immediately resign in disgrace!" Trump said.

Trump has proposed temporarily barring all foreign Muslims from entering the country and has advocated using water-boarding and other harsh interrogation methods.