MONTPELIER, Vt. (AP) _ Jesse Jackson won Vermont's presidential caucuses, according to official Democratic Party results released today.

Jackson edged Michael Dukakis by winning 596 of the state convention delegates elected at local caucuses last week. Dukakis won 582 delegates, while 120 were elected uncommitted. Albert Gore won four delegates.

The percentages were 46 percent for Jackson, 45 percent for Dukakis and 9 percent uncommitted.

Craig Fuller, executive director of the state Democratic Party, said the official tabulation had been slowed by mistakes found in some community caucuses. He said, for example, that in several communities, more delegates were elected than had been allocated to that town.

The delegates elected April 19 will attend the state Democratic Party convention next month at which time 14 of the state's 19 delegates to the national convention will be elected. The remaining five spots belong to Gov. Madeleine Kunin, a Dukakis supporter, and four party officials.

''In Vermont, more than in any other state, white people did not hesitate to vote for Jesse Jackson,'' Liz Blum, the Jackson state coordinator, said today. ''It shows how independent and thoughtful Vermonters are.''

Dukakis had won Vermont's non-binding presidential primary on March 1, receiving 56 percent of the vote to Jackson's 26 percent. Blum said she feels Jackson did better in the caucuses because ''it takes more of an effort to go to a caucus.''

William Wasserman, the Dukakis coordinator, said Jackson out-organized the Dukakis campaign. ''They organized in the smallest of communities, as well as the larger ones. That showed real persistence, real dedication to detail.''

Blum said the Jackson campaign would try to use its clout at the state convention to elect at least half of the delegates to the national convention and to pass resolutions supporting the Equal Rights Amendment and calling for reducing the military budget by $20 million and redirecting the money to a comprehensive cradle-to-grave health care system.