The Carter administration yesterday gave preliminary approval to an additional $250 million in federal loan guarantees to the ailing Chrysler Corp.

At the same time, the Chrysler Loan Guarantee Board issued a warning that the outlook for the auto company's recovery has become significantly more risky.

In Detroit, meanwhile, the American auto manufacturers yesterday reported that sales in early July showed evidence of a rebound from the very depressed sales levels in recent months.

In Chrysler's case, however, the damage done so far this year has proved to be worse than anticipated. The company yesterday reported a loss of $1.017 billion for the first six months of the year, thought to be the heaviest financial loss ever suffered by an American corporation for a half year.

The nation's third-largest auto company has been particularly hurt by the slump in auto sales, along with the uncertainity over its survival. h

Its sales this year have been below the levels called for in the government-approved recovery plan, and a new threat has arisen in the recent slackening in demand for its most popular cars, the subcompact Dodge Omni and Plymouth Horizon models. Sales of these cars in April and May (plus estimates for June) were 60 percent below totals for the first quarter.

Chrysler also told the government it has been unable to reach agreement with Mitsubishi Motors Company on financing shipments of Japanese-made cars and trucks which Chrysler sells in this country. Without a new agreement, Chrysler's cash needs this fall could be $150 million higher.

While acknowledging an increased risk of failure at Chrysler, the government loan board approved the $250 million second installment in federal assistance, saying it still believes Chrysler can recover if the company's new line of compact cars sells well next fall.

The board also authorized yesterday an additional $50 million in loan guarantees above the $250 million figure, if Chrysler can obtain an equal amount of aid from private sources.

Chrysler already has borrowed $500 million of the $1.5 billion in loan guarantees authorized by Congress.

Treasury Secretary G. William Miller, chairman of the loan board, said yesterday that government analysts now believe Chrysler will have to borrow a total of $1 billion in 1980 instead of the $800 million in guaranteed loans previously projected. The company is expected to borrow $200 million more in 1981, leaving $300 million of the $1.5 billion as a "cushion" against further possible setbacks.

"We expect them to be in the black in the fourth quarter," Miller added. Chrysler's overall 1980 loss is now forecast at $1.2 billion, about $150 million worse than an estimate on June 24, when the first loan guarantees were approved.

The board released excerpts of a report by the Booz Allen & Hamilton consulting firm warning of "considerable" risks that Chrysler's sales in 1980-81 will not recover sufficiently to keep Chrysler going.

Chrysler must sell its entire production of subcompacts and new K-model compacts beginning this fall to survive, according to the Treasury analysts.

But Miller, was encouraged by a recent improvement in Chrysler's sales and a strong advance demand by fleet operators for Chrysler's new compacts.

Overall, U.S. auto manufacturers reported early July sales only 19 percent from the same period last year, extending their rebound from May's dismal results. The five companies delivered 156,252 cars, compared with 169,936 in the first 10 days of July 1979. This year's period had one more selling day, so the percentage comparison is based on sales per day.

It was the first reporting period since March that sales showed a decline of less than 20 percent compared with a similar period in 1979.

Associated Press reported the following:

For the first time in te 1980 model year, truck sales by the Big Three companies rose. Ford Motor Co. and General Motors Corp. were offering large rebates on light-duty models, but Chrysler Corp. was not.

The annualized selling rate of the domestic industry rose to 7.0 million cars, compared with 5.5 million in June and 5.2 million in May. The annual rate is an estimate of what a year's sales would be if the selling period were characteristic of a typical year. Imports would add an estimated 2.2 million to the figures for each month.

The rate was close to 11 million for combined domestic and import sales before credit controls, now dismantled were imposed in March. Actual 1979 sales were 10.6 million cars, 8.3 million domestic.

Though ever-optimistic sales executives have been saying the industry had bottomed out, early July sales clearly were better than expected.

Ford, which ended rebates just after the period closed, sold 45,884 cars, off 14 percent from 46,732 sold in last year's period. GM, which had no car rebates, sold 88,462, down 22 percent from 98,991; Chrysler, which ended car rebates in June, sold 14,463 cars, down 23 percent from 16,383.

American Motors Corp., which ended rebates July 5, sold an estimated 3,700 cars, off 16 percent from 3,837; and Volkswagen of American sold 3,743, up 9.4 percent from 2,993. AMC reports actual sales only once a month.