The government issued new welfare rules yesterday that will cut the benefits of almost one of five families that receive them, saving the federal government $6 billion and the state governments about $5 billion over the next five years.

About 408,000 of the 3.9 million families who receive money under the Aid to Families with Dependent Children program will lose all their benefits. Another 279,000 will suffer some cuts when the rules take effect Oct. 1. The benefits to about 16,000 families are expected to increase because of some technical changes in the rules.

The regulations, issued by the Health and Human Services Department, will put into effect proposals made by President Reagan and enacted by Congress in the massive budget-cutting reconciliation act last summer.

Welfare groups, labor unions and many local and state government officials bitterly opposed the welfare changes during the legislative fight, but Reagan pushed them through Congress in a series of legislative victories. His purpose was not merely to save the government money, but to tighten up practices or overly permissive rules that, Reagan administration spokesmen said, let people receive welfare when they were able to find work or had sufficient income or resources to support themselves.

Financially, the most important new rules issued yesterday cut back the "earnings disregards," the amount of a welfare applicant's income that is spent on work-related expenses and that can be deducted in determining his benefits. For example, in some states a person was allowed to deduct $150 or more a month in work expenses; so if his income was $450 and his expenses $150, the person was considered to have income of only $300 for eligibility and benefit calculations. The higher the amount that is excluded, the lower the person's final income will be and the higher the benefits.

Here are the key changes:

* The regulations set up a fixed system of disregards that the states may not exceed, consisting of a basic work-expense deduction of $75 a month for employed welfare clients, up to $160 a month in child-care expenses for each child, and for four months, another basic $30 deduction plus one-third of the remaining earnings. These limitations, smaller than those now applicable, will save the federal government nearly $2 billion over the next five years.

* The regulations bar AFDC to families with incomes exceeding 150 percent of the state's "standard of need," the amount the state thinks is the minimum amount needed to live on.

* The regulations allow states to count public food stamp and housing subsidies received by a family as income, require states to count step-parent income as part of family income in determining eligibility, and require them, in effect, to spread out calculations of income based on things like inheritances.

* The amount of assets a family may have and still be eligible for welfare will be $1,000, not counting its house, a reasonably priced car and, at the state's option, certain items essential to living such as clothing and furniture. The previous limit was $2,000.

* States are forbidden to make payments to pregnant women before the sixth month of the pregnancy; they are permitted to institute "workfare" programs to give people on welfare work experience; aliens will be eligible for welfare only when they are in the country lawfully; states are forbidden to pay welfare to strikers; states are forbidden to pay support to a dependent child unless he is under 18, or under 19 if in school (the previous school cutoff was 20).