The Prince George's County Library Board has agreed to an extra holiday and two more days of sick leave for the county's 336 library workers, who have been protesting plans to extend their work week without increasing their pay.

The board announced the changes after a 3 1/2-hour meeting Thursday night with the library staff association.

Last week, petitions with 253 names of library workers had been presented to the board, opposing the longer work week.

Under the compromise acceptable to both sides, the increased work week, from 37 1/2 to 40 hours, will go into effect as scheduled Jan. 1.

To offset this, the employes will get Martin Luther King's birthday off and two additional sick days a year, starting in 1984.

They will also receive a 6.25 percent increase in accumulated annual and sick leave this year.

The board further agreed to consider paying meal money for employes working evenings and Saturdays and to review the entire work schedule as part of the yearly budget process beginning July 1, 1984.

"We feel the library board was responsive to staff concerns and think the decisions made are in the best long-term interests of the library system," the staff association leadership said in a written statement after the meeting.

William Gordon, the library administrator who first proposed the longer work week, said he was also satisfied with the outcome, which is expected to be ratified Oct. 13 at the board's next official meeting.

He said he had proposed the longer work week earlier this year because of budget constraints.