Chrysler Corp. reported a second-quarter loss of $536.1 million yesterday, bringing the total losses for the American auto industry this year close to $2 billion.

There was a trace of silver lining to the bleak financial report for Chrysler, however. A slight improvement in car and truck sales recently left the No. 3 automaker with a $981 million loss for the first half of 1980, $32 million less than the company had projected two weeks ago.

"While this does not suggest a permanent turnaround, the tone is upward," Treasury Secretary G. William Miller said yesterday.

The Chrysler Loan Guarantee Board, headed by Miller, gave formal approval yesterday to $300 million in additional federal loan guarantees to help keep Chrysler afloat during the balance of 1980.The board so far has approved loan guarantees of $800 million out of the $1.5 billion authorized by Congress last year.

The $300 million is to be raised through a public offering of 10-year notes bearing an 11.14 percent interest rate and due July 15, 1980. The notes, which are not redeemable for three years, are backed by Chrysler collateral estimated at $2.2 billion by Treasury analysts, as well as by the government's guarantee.

The second installment for Chrysler also was approved yesterday by the Senate Banking Committee but not without another gloomy forecast from its chairman, Sen. Williams Proxmire (D-Wis.), who is the most persistent congressional critic of the rescue plan.

He contended there is "strong evidence . . . that the company's financial situation is worse than ever and progressing steadily downward." The continued congressional support for "chrysler is based on "politics and pious hopes," he said.

Chrysler's second-quarter loss of $536.1 million compared with a $207.1 million loss for the second quarter a year ago.

The half-year loss of nearly $1 billion is believed to be the greatest ever for an American corporation.

Chrysler was not alone. General Motors Corp. had a second-quarter loss of $416 million domestically, while Ford Motor Co. reported a $468 million loss for U.S. operations over the same period. American Motors Corp. reported a $84.9 million loss, its greatest three-month deficit ever.

GM's loss for 1980 so far now totals $257 million compared with $631 million for Ford and $86.3 million for AMC, Both GM and AMC were profitable in the first quarter of this year.

Chrysler's hopes for survival depend upon a successful introduction this fall of a new line of compact, front-wheel drive cars and upon a rebound in auto sales from the recession levels of the first half of 1980. Chrysler sold 299,694 vehicles worldwide during the second quarter compared with 485,564 during the second quarter of 1979.

"Fortunately for Chrysler, our difficulties should soon be overcome with the introduction of our new 1981 line of cars and trucks," Chrysler Chairman Lee A. Iacocca said yesterday.

"Assuming a modest upturn in the economy, we expect to report an operating profit in the fourth quarter," he added.

United Press International reported the following:

Allied Chemical Corp. yesterday reported an 86 percent gain in second-quarter profits to a record $73 million ($2.02 a share) on sales of ($1.37) a year ago on sales of $938.9 million.

First-half profits were $141.2 million ($4.08) on sales of $2.748 billion compared with $67.1 million ($2.35) a year ago on sales of $1.738 billion.

Chairman Edward I. Hennessy Jr. said gains from Allied's interests in North Sea oil, Indonesian natural gas, fertilizer chemicals and soda ash more than made up for weakness in plastics and fibers and automotive products.