WASHINGTON  President Obama issued orders to send about 30,000 additional American troops to Afghanistan as he prepared to address the nation Tuesday night to explain what may be one of the most defining decisions of his presidency.

Mr. Obama conveyed his decision to military leaders late Sunday afternoon during a meeting in the Oval Office and then spent Monday phoning foreign counterparts, including the leaders of Britain, France and Russia.

Robert Gibbs, the White House press secretary, declined to say how many additional troops would be deployed, but senior administration officials previously have said that about 30,000 will go in coming months, bringing the total American force to about 100,000.

On top of previous reinforcements already sent this year, the troop buildup will nearly triple the American military presence in Afghanistan that Mr. Obama inherited when he took office and represents a high-stakes gamble by a new commander in chief that he can turn around an eight-year-old war that his own generals fear is getting away from the United States.