Officials of the Office of Management and Budget, which for three years has been playing St. George to the federal paper-work dragon, said yesterday that the dragon is bigger than they originally thought but that their efforts to cut him down to size have been successful.

To be more exact: for the first time, the OMB plans to include the contract-related paper work done by firms selling soap, submarines, satellites and other goods to the government as part of the government paper-work burden. That brings to 2,023,000,000 hours the time that the OMB estimates businesses and individuals spend each year compiling information required by the government.

For the OMB, the good news is that in fiscal 1983 its efforts to cut red tape saved people 144 million hours they otherwise would have spent filling out forms. The bad news is that, thanks largely to the addition of the procurement paper work, the total estimated time the nation spent filling forms grew by nearly 60 percent.

"There has never been a government-wide effort to control paper-work burden on those who do business with the government," said Christopher C. DeMuth, administrator of information and regulatory affairs for the OMB. DeMuth added that the government's three major procurement agencies--the Defense Department, the General Services Administration and NASA--have agreed to try to cut their paper work by 10 percent in fiscal 1984.

"This is the first-ever government process to calculate the private-sector cost of government policies," De Muth added, referring to the OMB's three-year-old crusade to reduce the information government agencies seek, such as the information the Agriculture Department asks of farmers, the Energy Department asks of oil companies, or the Internal Revenue Service asks of taxpayers.

Before procurement was added to the government-wide figure of paper-work "burden-hours," the Treasury Department (the IRS' parent agency) generated more than half of the total paper-work burden, according to OMB figures. Now, however, Treasury takes second place (29 percent of the paper-work burden) and the Defense Department, the biggest customer in the federal government, takes the lead (31 percent).

Asked if any government-generated paper work does not fall under the OMB's authority, DeMuth cited two categories: paper work required of federal employes, and notices (like the surgeon general's health warning on cigarette packs), the wording of which is required by law.

Observers such as David Marsh, director of a business group that has fought its own battle with paper work for more than 40 years, offered restrained praise for the OMB's efforts. "I think we're making progress, but this procurement thing is going to be a tremendous undertaking," Marsh said.

"My members are saying: 'We've been through this a long time, now we want to see some good solid results.' But the last thing I want is DOD picking out which forms it's going to cut . They might pick picayune ones that aren't a real problem," he said.

Robert Greenstein, director of the Center on Budget and Policy, offered a different criticism. Noting that the OMB's report cited paper-work savings in the food stamp program, he said: "There's no question that virtually every food stamp or welfare office in this country will tell you their paper work is up."