Under gray skies and a sprinkling rain that beaded on badges taped in black, the holders of the city's highest offices--and some others mourners who are being held in its jails--gathered yesterday for the funeral of Delbert C. Jackson Jr., the D.C. corrections department director.

"We ought to look at this as a celebration of Del Jackson's life," said Mayor Marion Barry from the pulpit of the Nineteenth Street Baptist Church.

In the audience of several hundred mourners were Jackson's widow and children, other family members, personal friends, government officials, City Council members and a small group of inmates who had come to sing in Jackson's honor.

Jackson died of intestinal bleeding last Wednesday at Washington Hospital Center. He was 52.

"Delbert Jackson was a caring individual. He was not called to be an indifferent superintendent of a human warehouse," said Barry.

Before Barry and other officials spoke, the soft voices of the Mighty Songs of Joy--seven inmates of Lorton Reformatory, the prison Jackson ran--sang "The Lord's Prayer" and "Amazing Grace" in a capella tribute.

Throughout the church at 4606 16th St. NW were somber corrections officers in uniform blue and polished shoes, the black tape over their badges symbolizing the traditional salute of the law enforcement community for the death of a comrade.

City Administrator Elijah B. Rogers said Jackson, an employe of the corrections department since 1964 and its director since 1972, had made "the commitment we all must make to be the true trustees" of the public welfare. "Words are always the most impoverished medium to express the sentiments of the heart," Rogers said.

D.C. Del. Walter Fauntroy said Jackson's "compassion, competence and commitment will be missed" in a time when economic problems have forced reductions in programs for inmates. "Through it all he remained a man of conscience."

The Rev. H. Albion Ferrell of the city's Board of Parole gave the principal eulogy for Jackson, whose flag-draped coffin was surrounded by hundreds of flowers that contrasted, in their evocation of spring, with the overcast skies outside.

"It seemed to me Delbert Jackson had a deep understanding of the pulse of the people," said Ferrell.

Ferrell praised Jackson for the "recognition of the fact that these people [at Lorton] had not lost their humanity. They may have been rejected by their fellow man but they had not been rejected by God."

The Rev. Jerry A. Moore Jr., pastor of the Nineteenth Street Baptist Church and a member of the City Council, officiated at the service. Jackson was buried in Fort Lincoln Cemetery in the suburban Maryland community of Brentwood on Bladensburg Road.

A memorial service organized by former inmates will be held at noon today at the Martin Luther King Library, Ninth and G streets NW.