Donna Brazile, deputy national field director of the Dukakis campaign, resigned last night after telling reporters covering the campaign that they should pursue rumors, which she did not document, about Vice President Bush's personal life. In resigning, she said: ''Today I made certain comments which I deeply regret. I believe too strongly in the importance of electing Mike Dukakis and Lloyd Bentsen to allow myself to become an issue in the campaign. Because the time is short, and the issues are so important, I have decided to leave the campaign. I wish Mike Dukakis and Lloyd Bentsen the best in the final weeks of the campaign.''

Paul Brountas, chairman of the Dukakis campaign, told reporters tonight that Ms. Brazile had ''voluntarily resigned'' and that she ''regrets'' the remarks. ''She does not speak for the campaign,'' he added, ''and she did not speak for the campaign when she made those remarks.'' Mr. Brountas said Mr. Dukakis ''saw Vice President Bush tonight and he apologized for those remarks.''

Before her resignation, Dayton Dunan, Mr. Dukakis's press secretary, said ''Donna was not speaking on behalf of the campaign in any way whatsoever.''

Vice President Bush's press secretary, Sheila Tate, said ''The Bush campaign has no comment, no reaction.''