ANDOVER, Mass. (AP) _ Both Gillette Co. and the investor group battling to win four seats on its board hinted at victory Thursday as the scramble for shareholder votes gave way to the ballot count that will determine the winner.

Shareholder proxy ballots were filed Thursday at Gillette's annual meeting, a key step in the four-month effort by Coniston Group force a sale or merger of the Boston-based personal products company.

Although preliminary results are not expected for at least a week, both Coniston principals and Gillette executives expressed optimism they would prevail.

''Obviously, we think we will win,'' Coniston principal Augustus K. Oliver said after the three-hour annual meeting at which several shareholders drew applause for criticizing New York-based Coniston. ''We think we're ahead and we're looking forward to the results.''

Although Coniston would control only one-third of the board if successful, Oliver said a Coniston victory would constitute a shareholder mandate for the group's agenda.

Colman M. Mockler Jr., Gillette's chairman and chief executive, declined to give specific projections but stated: ''We are pleased with the results so far.''

Gillette rose $1.50 to $41.75 a share in composite New York Stock Exchange trading.

The contest likely will be decided by institutional investors, such as pension funds and insurance companies, which own between 60 percent to 65 percent of the 115.5 million Gillette shares outstanding.

Coniston controls 6.76 million Gillette shares, about 5.8 percent of the company's shares outstanding. Coniston also claims to have the support of several major shareholders.

Since early March, both sides have been battling in the courts and the press while seeking support from the company's nearly 27,000 shareholders.

In a final presentation at Thursday's meeting, Coniston principal Paul E. Tierney Jr. told nearly 800 shareholders their investments would produce large financial dividends through the sale of Gillette's corporate empire.

Tierney also said Coniston would remove provisions designed to shield the company from takeovers and to protect top management posts.

Oliver said the group seeks to sell the company as a whole entity, except for the possible divestment of some divisions. In the meantime, he pledged to devote more corporate resources to research and development and product marketing.

Oliver said no potential buyers have approached Coniston so far, although he indicated the group would consider a proposal by Revlon Group Inc. Revlon in November 1986 abandoned repeated attempts to take over Gillette after receiving a nearly $580 million stock repurchase, and signed a 10-year pact not to seek control of the company.

Mockler, one of the directors whose seat is being challenged, denied published reports that six suitors hade signed an agreement to purchase the company.

Mockler and other Gillette officers gave presentations stressing the company's worldwide growth and increased profitability since its restructuring and dismissal of 2,400 workers after signing the Revlon pact. No mention was made of plans to close plants or further reduce its 30,000-member workforce.

In addition to the proxy fight, Gillette and Coniston are entangled in legal battles. Gillette is attempting to have the results of the shareholder vote invalidated, and Coniston has sued Gillette for allegedly using false and misleading information in its campaign to win shareholder votes.

Coniston nominated Oliver, Tierney, Coniston principal Keith R. Gollust and former cable television executive David Strassler for three-year director posts.

In addition to Mockler, the company placed Gillette directors Lawrence E. Fouraker, Herbert H. Jacobi and Joseph F. Turley on the ballot.