President Reagan announced yesterday that the government will hire at least 1,200 new investigators and prosecutors, as well as support personnel, to escalate the administration's war on narcotics and "expose, prosecute and ultimately cripple organized crime."

"The time has come to cripple the power of the mob in America," Reagan said. "The American people want the mob and its associates brought to justice and their power broken. Not just out of a sense of vengeance but out of a sense of justice.

"As all of you know," the president said, "crime today is an American epidemic. It takes the lives of over 20,000 Americans a year, it touches nearly a third of American homes and results in about $8.8 billion a year in financial losses."

FBI Director William H. Webster said organized crime reaches throughout society, including law enforcement and public figures.

Attorney General William French Smith added that illegal drug sales in 1980 were "more than $79 billion . . . about equal to the combined profits of America's 500 largest industrial corporations."

Senior administration officials, who asked not to be identified, said the additional investigators and prosecutors will be deployed in 12 new regional task forces covering the country at an initial cost of $160 million to $200 million. The administration will seek the money in an amendment to the 1983 budget that will be sent to Congress as soon as it returns for the lame-duck session in late November, the officials said.

But a Justice Department official said the overall 1983 budget will not be increased. He said the administration will ask that funds be transferred from agencies not involved with law enforcement, and said the president has not decided what programs would be cut.

The Drug Enforcement Administration now has just over 1,800 agents. About 500 of the FBI's 7,800 agents also are working on narcotics cases. Government sources said that about 600 to 700 of the new positions will be for FBI and DEA, 200 will be prosecutors, and the rest will be scattered among other agencies.

Reagan's announcement in the Great Hall of the Justice Department yesterday was greeted by a standing ovation from hundreds of federal law enforcement officials gathered there for the occasion. But behind the scenes, some of the officials said that while welcoming the extra manpower they are worried about how the new task forces will operate.

Modeled loosely on the anti-drug task force that has been operating in southern Florida for about the last six months, they are to be centered in 12 key cities: Boston, New York, Baltimore, Atlanta, Houston, St. Louis, Chicago, Detroit, Denver, Los Angeles, San Francisco and San Diego.

Federal authorities in Baltimore would not discuss the task force plan as it would affect the Maryland-Washington region. They said they would provide details at a news conference today where the Baltimore head of the FBI and the U.S. attorney will make a joint announcement.

One FBI source said that while the FBI does not yet know how many agents will be assigned to the region, approximately 65 percent will be FBI and 35 percent will be DEA. The U.S. attorney for Maryland, J. Frederick Motz, said he thought the number of agents/prosecutors for the region--which will include Maryland, Virginia, the District, Delaware and the eastern two-thirds of Pennsylvania--would range from 80 to 100 agents and 15 to 20 prosecutors.

The FBI source said the operation will be a "task force" only in the sense that Baltimore-based agents and assistant U.S. attorneys will work exclusively on drug-related crime and will deal with their colleagues beyond the Baltimore region on a regular basis.

The administration will use agents from the FBI, the DEA, the Customs Service, the Immigration and Naturalization Service, the Internal Revenue Service, the Coast Guard and other agencies in the task forces.

Some officials in the Justice Department expressed concern about rivalries in such broad-based task forces among different agencies, about keeping investigations secret with so many people involved, and about the possibilities for corruption when so many agents and agencies are involved.

Some officials also questioned the timing of the announcement less than three weeks before the Nov. 2 elections and speculated that it was politically motivated. Associate Attorney General Rudolph Giuliani denied that the announcement was meant to help Republicans at the polls.

Just last year, the administration attempted to cut budgets for federal law enforcement. Smith successfully fought behind the scenes against the cuts for the FBI and the DEA, both under the Justice Department.

Under the new plan announced yesterday, administration officials said they expect to arrest 700 to 800 more criminals a year, but it is not clear where they would be imprisoned. One high-level official said the government will spend $20 million to expand federal prison facilities to accommodate 1,200 to 1,500 additional prisoners.

Meanwhile, he said, there are plans to spend $8 million to $10 million to lease space in local, non-federal prisons. "There are plenty of places available," he first said, but then conceded that local jails are currently overcrowded and the government has no survey of available space.

Reagan, citing Senate investigations in the 1950s and 1960s that spotlighted organized crime, said he would set up a panel to make a three-year study of organized crime's influence in every region of the country. Governors will be asked to join the effort by coordinating federal and state programs, he added.

In addition, Reagan created a Cabinet-level committee on organized crime under Smith to coordinate all federal efforts and keep the president current. The president will require the attorney general to submit an annual report to him and Congress on progress in the fight against organized crime and drug trafficking.

Another part of the crime program would establish a national center to train local law enforcement agents to combat such relatively new types of organized crime as arson, bombing, bribery, computer theft, contract fraud and bid-rigging, as well as drug smuggling.

In a radio speech last week, Reagan said he was planning a "bold, confident" attack on drug smuggling. The idea would be to prevent traffickers from simply moving to another location when law enforcement activity increased in their city, he said.

"We're going to be waiting for them," Reagan said. "We're not just going to let them go somewhere else. We're going to be on their tail."