NEW YORK, Nov. 19 -- U.S. District Judge Edward Weinfeld, weakened by a fall in front of the federal courthouse in Manhattan, said today that he was not certain he could complete the seven-week-old trial of Charles Agee Atkins, who is charged with running a fraudulent tax shelter scheme that generated $350 million in allegedly phony deductions for wealthy investors.

Weinfeld, who suffered severe cuts and bruises a few days ago when he tripped on a crack in a sidewalk, is 86 and the oldest sitting federal judge. Lawyers hold him in high regard for his razor-sharp mind, legal skills and judicial fairness.

A rarely invoked court rule provides that when a judge who has begun a trial can no longer preside, the case can be taken over by another judge who certifies that he is familiar with the record.

Weinfeld had set today for the start of closing arguments by attorneys for the government and for Atkins and his two codefendants, but he tentatively rescheduled the summations for Monday.

His face marred by large bruises, he told the jury he had come to court "over the vigorous protests of my doctors and my family."

Expressing his respect for the "extremely conscientious" jurors, he told them: "I started the case. I want to finish the case. I actually don't know if I can."

Atkins, 32, the son of former Ashland Oil Co. chairman Orin E. Atkins, filed for protection under the bankruptcy code in May 1984. The government has said that his cluster of tax shelters, collectively called The Securities Groups, brought off the biggest tax fraud of its kind in history.

Atkins is a former partner of Edward A. Markowitz, a Washingtonian who in 1985 pleaded guilty to four tax fraud counts relating to a similar tax shelter scheme he operated and who is a part owner of the Washington Capitals hockey team. Markowitz awaits sentencing after testifying for the government in October. Atkins' codefendants are William S. Hack, 62, and Ernest M. Grunebaum, 52.