Mitt Romney, the 2012 Republican presidential nominee, will address a gathering of Republicans in California this weekend that will mark his first public comments since making it known that he may run again in 2016.

A Republican official said on Tuesday that Romney will give brief welcome remarks at a reception during the Republican National Committee's annual meeting in San Diego on Friday.

The gathering brings together state Republican Party officials from across the country. Other potential 2016 candidates expected to appear are Wisconsin Governor Scott Walker, former Texas Governor Rick Perry and conservative physician Ben Carson.

Romney surprised the political world last Friday by telling a private donors meeting in New York that, according to sources, he wants to be president and that he is considering a run.

Those close to Romney say he will make up his mind in a matter of weeks.

"I think sooner rather than later," said a Romney adviser. "He realizes there's a window and you want to make sure that you make a timely decision."

Romney would be making a third run for the White House, a prospect that many Republicans doubt would be successful.

But those close to Romney say he feels the other leading establishment figure who is leaning toward a run, former Florida Governor Jeb Bush, would be vulnerable in a race against Democrat Hillary Clinton, who is expected to seek her party's presidential nomination.

(Reporting By Steve Holland; Editing by Alan Crosby)