The nation's prison population is at a record high, with the rate of new inmates in 1981 running at more than double the rate for 1980, a government report says.

The Bureau of Justice Statistics reported yesterday that state and federal prison populations swelled by more than 20,000 in the first six months of 1981, more than were added in all of 1980 and an "unprecedented growth rate," according to Carol Kalish, the statistician who compiled the report. The prison population reached a record 349,118 inmates on June 30 of this year.

The statistics spotlight the Reagan administration's offer of $2 billion in federal funds to help states build new prisons to house their growing numbers of inmates. While there is no money officially in the budget, the states have been told by the Justice Department that the federal government will finance construction of new prisons if the states provide matching funds.

The federal prison population rose by 1,370 to 25,733 in the first half of 1981, reversing a trend that had reduced federal inmate numbers by one-fourth in the last three years. Said the Bureau of Justice Statistics report: "Federal authorities attributed this change to more aggressive law enforcement at the federal level and to a more conservative federal parole policy."

The increase of almost 19,000 in the state prison population was attributed to a variety of factors, including tougher sentencing legislation. In the past four years, 37 states passed mandatory sentencing statutes and 15 states passed determinate sentencing laws that send violent offenders to prison for a fixed number of years that cannot be shortened by parole.

Four states -- Indiana, Illinois, Maine and New Mexico -- have passed laws that have done away with parole completely. New York and California are the two largest states that have passed habitual-offender legislation that mandates jail terms for people who have committed a second or third offense.

Many state prisons are now taxed to their limit by their inmate populations. There are 30,954 prisoners in Texas state prisons, some of them sleeping on floors and living in tents. Other state prisons house inmates in prefabricated buildings and abandoned military barracks. Some states have resorted to double-bunking to cope with their prison populations.

"Facilities in some states housed almost twice their rated capacity," the Bureau of Justice Statistics report said, "and other states were relying heavily on space in local jails."

The states with some of the largest prison populations showed some of the largest percentage gains. The number of inmates in California state prisons rose nine percent in the first half of 1981. In Georgia, the rate of increase was 9.7 percent and in New York 10.7 percent. Prison populations also showed big gains in Alabama, Ohio and Indiana, which is now admitting to its prisons 100 more inmates a month than are being released.

Only four states -- Colorado, Minnesota, New Mexico and Oregon -- managed to lower their prison populations in the last year. Colorado passed a presumptive sentencing law in 1978 that reduced the average sentence; Minnesota's new sentencing guidelines take prison capacity into account and Oregon is under a court order to increase its reliance on probation to hold down its inmate count.

New Mexico's prison population is down for two reasons. The riots that took place in New Mexico prisons in 1978 and 1980 forced the transfer of some state prisoners to tougher federal prisons and resulted in a rising use of probation that lowered by 17 percent the number of inmates assigned to minimum-security prisons.

The rate of growth for women inmates exceeded the rate of growth for men. The number of women put in prison in the first half of 1981 grew at a rate equal to 22 percent a year. The number of women in prison at the halfway point in 1981 was 14,656, a gain of 1,400 in six months and the most ever recorded since 1925, when statistics were first kept on prison populations.