Victor A. Schroeder resigned yesterday as president of the Synthetic Fuels Corp. following a public dispute with fellow board members who had accused him of mismanagement and improprieties in office.

Schroeder alluded only briefly to these allegations in his resignation letter, saying that in recent months "board dissension has been apparent and focused on my role as president and chief executive officer."

He said stepping down was "a difficult decision" but part of "a sincere effort to help the board and the corporation focus attention on the important issues facing the development of a domestic synthetic fuels industry."

Schroeder, 62, decided to leave the $135,000-a-year job under mounting pressure from three of the corporation's seven directors, who publicly urged his dismissal and were preparing to push for his ouster at a special board meeting Aug. 29.

The former Atlanta developer, named to the board by President Reagan, said he would continue through 1987 as a part-time director, a position carrying a $10,000 salary.

The dissident directors had complained that the full-time board members--Schroeder and his longtime associate, Chairman Edward E. Noble--ran the federally funded corporation as a family business and froze them out of most major decisions.

The shake-up could break the recent impasse at the 3-year-old public corporation, which has made little progress in its effort to finance development of alternative energy sources. Although Congress has given the corporation $15 billion to invest in new technology, the corporation approved the first project only last month.

Schroeder initially appeared determined to keep his job, saying that he had done nothing wrong and that his actions had been "twisted" by "duplicitous" people opposed to his policies. His resignation means the directors can name one of their own as president or find a replacement from outside the corporation.

The controversy escalated last month when a corporation official told a Senate hearing that Schroeder had offered another director help for his private business in return for the director's support for a Schroeder plan to reorganize the corporation. The corporation's inspector general has referred the allegation to the Justice Department.

The Senate subcommittee on oversight of government management also found that Schroeder awarded 51 consulting contracts without competitive bidding, some of them to former business associates.

In addition, an inspector general's audit found that Schroeder improperly charged the corporation more than $25,000 for interest payments and a broker's fee on purchase of his Alexandria home. Schroeder later repaid the $19,500 broker's fee.

Subcommittee Chairman William S. Cohen (R-Maine) said that Schroeder's resignation "reflects his concern for the best interests of the corporation" and helps end "an almost irreconcilable situation."

"The board of directors was so polarized that it was in danger of becoming paralyzed," Cohen said.

Board member Robert A.G. Monks, Schroeder's most outspoken critic, praised him for reaching "a difficult and statesmanlike decision that makes it possible for the corporation to turn its focus to different subjects and to move forward."

Cohen had been highly critical of a late-night meeting in New York last March between Schroeder and board member Milton M. Masson Jr. Schroeder has said that he sought and received Masson's support for Schroeder's reorganization proposal.

During the same conversation, Schroeder acknowledged, he agreed to contact a friend at Mobil Land Development Corp. to find out whether the oil company subsidiary had any business that might be performed by Masson's engineering design firm.

Masson supported Schroeder's plan at a board meeting the next day, and Schroeder later called the Mobil Land official. Both men maintained that the actions were not connected, but a witness to the conversation, corporation official Donald Thibeau, said it was clear that Schroeder and Masson "came to an understanding" on the two matters.

"It looked like vote trading," Cohen said. "You scratch my back, and I'll scratch yours--that was the appearance."

But Schroeder said he saw no conflict of interest, even if the land company's parent firm, Mobil Oil Corp., were to seek funding from his agency.

Schroeder, whose wife will continue to work as Noble's secretary, said his tenure since 1981 has been "marked by tangible success in shaping this organization." Cohen, however, said Congress expects to see much greater progress if it is to extend the corporation's authorization.

The corporation expects to finance production of fewer than one-third of the 500,000 barrels of fuel a day that Congress has mandated for 1987. Corporation officials say the market for synthetic fuels has been hampered by high interest rates and falling oil prices.