While the Reagan administration's fiscal 1984 budget would leave most domestic agencies struggling to keep up with inflation, the Justice Department budget would be increased by 10 percent, with most of the increases assigned to the president's war on drugs and organized crime, additional federal prisons and new computer technology.

In seeking the largest increase for federal law enforcement in more than a decade, Reagan would raise the total Justice Department budget from just under $3 billion to $3.3 billion. The FBI budget would go up by nearly 25 percent to over $1 billion for the first time.

Included in the FBI increase is $800,000 and 25 new positions for a "hostage rescue team," which Justice officials described as a highly trained unit with capabilities far beyond those of existing FBI special weapons and tactics (SWAT) teams. It would be a mobile unit, based in Washington, and could be used in hostage or terrorist situations.

The FBI also would get a major increase in agents and funding in the area of foreign counterintelligence, but the exact numbers are classified.

The administration has asked for about $185 million--with some of the money in the Treasury Department budget--for the 12 regional task forces being set up to investigate and prosecute high-level drug and organized crime operations. That funding would allow the hiring of 1,600 new employes at Justice and Treasury, including agents, prosecutors and support staff.

The proposed budget also seeks $96 million for new prison construction. Justice officials say that they plan to build two new 500-prisoner facilities in the Northeast, but the sites have not been determined. In addition, there is a provision for a new prison for 500 inmates in Los Angeles. Another $10 million is included for renovating existing federal prisons to expand their capacity by 340.

The department wants to spend $175 million on new technology, much of it for new computer systems at the FBI, the Drug Enforcement Administration and the Immigration and Naturalization Service. The FBI also has funding for a new secure communication system that will prevent outsiders from listening in. The budget also includes $90 million for a new state and local matching grant program in the area of criminal justice.