LONDON—Mitt Romney launched an overseas tour Thursday that injected a dose of national security into a presidential race that has been nearly devoid of it.

But in his first day of official visits with British leaders, the presumptive Republican nominee had to deal instead with a flap that followed comments he made about British preparations for the Olympics that ruffled feathers and drew a dig from London's mayor.

Mr. Romney was referring, in part, to the failure of a private contractor to provide enough security guards for Olympic venues, requiring the U.K. government to bring in additional troops.

That distracted, at least to some extent, from the campaign's broad goal for the trip, which was to present Mr. Romney as a statesman operating smoothly on the world stage.

Mr. Romney opened his overseas effort, which also will take him to Poland and Israel, by holding a round of meetings with dignitaries including Prime Minister David Cameron, former Prime Minister Tony Blair and Labour Party leader Ed Miliband. They discussed Europe's economic crisis, the Middle East peace process and growing tensions in Syria and Iran.