Chrysler Corp., its back to the financial wall, received final approval from the government today to sell federally guaranteed securities and by afternoon had sold nearly all of the $500 million in notes it offered to investors.

"We're virtually done (placing the debentures), and we're in very good shape," said James D. Wolfensohn, general partner of Salomon Brothers, the investment banking firm that handled the Chrysler sale.

Chrysler has been so cash-short in recent weeks that it has had to stop paying its 19,000 suppliers until it could get additional money through the government-backed note sale.

Although the government agreed to guarantee the Chrysler borrowings months ago, the Chrysler Loan Guarantee Board, headed by Treasury Secretary G. William Miller, could not put its final stamp on the loans until all of Chrysler's 400 creditors agreed to restructure their debt agreements.

A number of small banks held out, but by last Friday, under heavy pressure from both the company and the government, all of Chrysler's creditors (the auto company owes about $4.4 billion to banks, insurance companies and the like) agreed to change the terms of their loans.

Even after the recalcitrant banks came into line, it seemed as if the fates continued to conspire against the nearly bankrupt company.

A five-alarm fire in a mid-town Manhattan skyscraper Monday night forced lawyers to flee the building and leave behind the huge amount of paperwork needed before the loan guarantee board could act.

But none of the papers were damaged in the blaze (which injured 125 persons, mostly firemen), and this morning the papers were moved to another office where they were verified through telephone hookup to Washington.

The notes, which carry an interest rate of 10.35 percent and mature in 1990, went on sale officially at 12:30 p.m.

Wolfensohn said interest in the notes -- which the government guarantees will be paid off whether or not Chrysler Corp. survives its financial difficulties -- was strong on the part of institutional investors such as pension funds and insurance companies and of individuals.

He said that there seemed to be a "strong nationalist" sentiment on the part of many investors, who wanted to buy the Chrysler paper to insure the survival of the nation's third biggest auto producer.

It will take more than sentiment, however, to keep the auto producer in business. Although the company can borrow up to $1.5 billion under the government program, it also must sell more cars.

Chrysler Chairman Lee A. Iacocca, who was president of Ford Motor Co. until 1978, has said that the survival of the company hinges on the success of the K-cars.

Chrysler has more than 130,000 employes, many of whom are on layoff because of the severe recession in the automobile market. The company made labor history last month when it added United Auto Workers President Douglas Fraser to its board of directors.