American Finance System, a consumer finance company based in Silver Spring, yesterday approved a new tender offer from Security Pacific Corp. that would equal $10 tax-free for each share of AFS.

The Los Angeles bank holding company, which originally proposed a stock transfer at the equivalent of 7.85 tax-free per share of AFS, sweetened its offer yesterday after a Miami company, Aristar, made a bid of $9.50 cash on Monday. AFS stock did not trade yesterday. On Tuesday, it rose to $8.25 in very heavy trading from its Friday close of $7.625.

Aristar President L. Gerald Wright said yesterday Aristar executives and attorneys and Gamble-Skogmo officials would have to evaluate the Security Pacific offer before deciding whether to make a counter offer. Gamble-Skogmo, the mass merchandiser, owns a controlling interest in Aristar, a consumer finance and furniture company.

AFS board unanimously rejected Aristar's bid on the grounds that it was not in the best interests of AFS shareholders. Aristar, which recently purchased 4.8 percent of AFS on the open market, has offered to buy up to 2.3 million shares, or enough to give it a 52 percent interest in AFS. Such a purchase of AFS stock for cash would be taxable.

Security Pacific's offer is a stock transfer for all AFS common stock. Under the revised merger plan, each share of AFS would be exchanged on a tax free basis for $10 market value of Security Pacific common stock determined by the closing price for Security Pacific for the 30 trading days preceding consummation of the merger. Each share of AFS preferred would be bought for $25.25 in cash plus accrued dividends.