Securities and Exchange Commission Chairman David S. Ruder said yesterday he has spoken with President Reagan only once -- on the telephone -- since the stock market collapse Oct. 19 and has not briefed him on the historic event.

Ruder, testifying as the Senate Banking Committee opened hearings into the record fall of the stock market on Black Monday, when the Dow Jones industrial average plunged 508 points, said he has briefed members of the White House staff but not the president.

Reagan phoned him the Saturday after the record-breaking drop and, during that conversation, commended the SEC for the work the agency had done that week, Ruder said.

Sen. Donald W. Riegle Jr. (D-Mich.) expressed surprise that Reagan did not receive a report from Ruder on the market collapse and said there was "a serious problem of presidential disengagement."

"I find that an astonishing fact and a disturbing fact," Riegle said. "We need all the confidence builders we can get right now. I think the situation is deadly serious and it is not over."

Another committee member, Sen. John Heinz (R-Pa.), agreed that the markets are fragile. He said that if the market develops a "recession psychology," the Dow Jones average could drop an additional 600 points.

The market has recovered some of the ground it lost last month, but prices have declined the past two days and professional investors are still nervous about the outlook. Yesterday the Dow fell 18.24 points, to 1945.29.

Some Wall Street executives have said Reagan's relatively low-key approach to the stock market crisis demonstrates a lack of leadership at a critical time. They have urged the president to take public actions that would bolster investor confidence by showing that the White House understands the nature of the crisis and is taking appropriate action.

Riegle challenged Ruder, who has been at the SEC for only a few months, to be more forceful in his dealings with the White House and Congress. "You are one of the few people here who can create a sense of urgency," Riegle said.

After yesterday's hearing, White House spokesman B.J. Cooper defended Reagan's low profile, saying it was a deliberate attempt to calm the financial markets. Cooper said Reagan was concerned that greater presidential involvement might indicate "a panic response to events on Wall Street."

Cooper said that Ruder has been in touch with White House chief of staff Howard H. Baker Jr. on a regular basis and that Baker has briefed the president. Ruder said at the hearing that his first contact with the White House on Black Monday was at 1:30 p.m., when he spoke with Baker.

Cooper also said Reagan reacted responsibly by naming a special task force, headed by investment banker Nicholas F. Brady, to investigate the stock market collapse and to make recommendations for reform within 60 days. Reagan met with the task force yesterday.

Other members of the task force named yesterday were John Opel, chairman of the executive committee of IBM Corp. and an expert on computer technology; James L. Cotting, chairman of Navistar International Corp., who will represent the interests of large corporations; Robert G. Kirby, chairman of Capital Guardian Trust Co., a money manager who will represent pension funds and other institutional investors, and Howard M. Stein, chairman of Dreyfus Corp., who will represent mutual funds and the small investors who are involved in the stock market through these funds.

The Brady Commission's staff director will be Harvard Business School professor Robert Glauber, who will be assisted by Harvard Business School professor David W. Mullins Jr.

In response to other questions at the Senate hearing yesterday, Ruder said that a preliminary review showed that small investors were treated unfairly on Black Monday. He said there was evidence that orders to buy and sell stock from small investors were not executed on an equal basis with orders from large investors.

He said that issue would be explored further, and that he also would investigate whether brokerage firms put their own interests, and trades, ahead of their clients.'

No major securities firms are having cash problems, Ruder said, but he added that the most important way to prevent another market collapse was to increase capital available to trade stocks. He said this was critical to ensure that there were buyers as well as sellers during unstable periods.

Ruder vigorously called for a bigger SEC budget, which could be trimmed as the administration and Congress work to lower the federal deficit. He said the agency lacks adequate resources to conduct a thorough investigation of the stock market collapse while continuing to carry out its regular responsibilities, such as monitoring brokerage firm activities. His predecessor, John S.R. Shad, often said the SEC should try to do more with less.

Ruder said that based on a preliminary analysis, computer-directed program trading strategies appeared to have added to the volatility of financial markets on Black Monday. The controversial technique involves the simultaneous trading of stocks and stock index futures contracts, such as the Standard & Poor's 500 futures index, which represents a basket of 500 stocks.

Ruder also implied that a panel of experts assembled by the Chicago Mercantile Exchange to study the market collapse was selected because they were likely to endorse the exchange's defense of stock index futures and program trading.

Ruder said that the SEC beefed up its monitoring efforts in the days preceding Black Monday because of the volatility in stock prices. He also said that while he promised in his Senate confirmation hearings to focus on prosecuting illegal insider trading, his "private agenda" has been to focus on the stock market's instability.

Committee Chairman William Proxmire (D.-Wis.) raised questions about Ruder's comment to reporters on Oct. 19 that it might be necessary to consider a temporary halt in trading. Proxmire said that some have blamed Ruder's remarks for exacerbating the market's fall that day by causing nervous investors, who feared a halt in trading, to sell stocks.

Proxmire said it appears that the proper course of action, if one wishes to halt trading in the midst of market chaos, is to halt trading, but not to talk about it publicly first.

Ruder responded by criticizing the media, saying they "did not report my remarks correctly." Although SEC officials have said that one wire service incorrectly reported Ruder's remarks, Ruder has confirmed that the report distributed by the widely followed Dow Jones news service was accurate.

Ruder said that his comments to reporters that day were made at a time when he "did not have in my consciousness what sort of day it would be." Later, Ruder said that in retrospect it would have been better if he had not made the remarks concerning a possible trading halt.

At the hearing's conclusion, Ruder, a former Northwestern Law professor, turned toward his wife and SEC officials seated behind him and said, "It was like a four-hour final exam."