Parents United for Full Funding, a parents' lobbying group that played a major role in getting large increases in this year's D.C. school budget, has called on candidates in the upcoming primary elections to support at least another $23 million increase next year.

Roderic V. O. Boggs, a public interest lawyer and spokesman for the 600-member group, said Parents United believes the school system will have to spend $336.7 million in the 1983 fiscal year to grant scheduled pay raises, keep all the programs it has now, and avoid any layoffs.

This amounts to a 7.3 percent increase despite school system projections of a further 2.8 percent decline in enrollment, which is expected to drop to 90,700 when the fall term begins on Tuesday.

To make improvements Parents United is seeking an additional $10 million, bringing its total hoped-for budget up to $346 million. The group says most of this extra money should be spent on more remedial classes, computers and security guards.

"We'd like politicians seeking office to commit themselves before the election so we know where we'll be heading next year," Boggs said, adding that his group will make public the candidates' positions on their request before the Sept. 14 primary.

With its position papers, budget analyses, and lobbying, Parents United played a major role in getting a $42 million increase in this year's school budget approved by Mayor Barry and the City Council. That budget now is awaiting final action by Congress.

In its proposals for next year the parents group says 15 schools should be closed because of declining enrollment. School Supt. Floretta McKenzie recommended 14 closings last spring, but after heated debate the school board shut only two.