The Prince George's County teachers union has reached a tentative agreement with the Board of Education that would raise starting teacher salaries to $19,000 and would make the county's beginning instructors among the best paid in the metropolitan area.

County teachers who earned starting wages of $15,738 this year are now the lowest paid in the region. After the second year of the new contract, if it is approved by union members, starting salaries would jump to $21,000.

According to sources, whose information was confirmed by union and school officials, the proposed three-year contract would provide a 6 percent across-the-board salary increase at the start of the 1986-87 school year, a raise of 8 to 9 percent the following year and a 7 percent raise the third year.

The tentative settlement will go before 200 union representatives for their recommendation Monday and then before the county's 6,000 teachers for a vote in two weeks.

Paul Pinsky, president of the Prince George's County Educators Association, said the union is pleased with the tentative agreement.

"They [the salaries] are not as much as teachers actually deserve," he said, "but I think it's a significant improvement for teachers, one which teachers in this county have long needed."

The tentative agreement reflects the increasing importance of education this year as a political force in the county, with elected officials campaigning on the issue and state legislators fighting in Annapolis for additional funds for county schools.

Yesterday's agreement emerged after a week of intense negotiations, the first show of progress during two months of slow contract talks. Teachers had originally proposed a starting salary of $20,000, but agreed to accept $21,000 beginning in the 1987-88 school year.

The agreement also reflects recent flexibility on the part of the school board, which had originally suggested a complex salary schedule with raises spread over the school year in seven steps.

The settlement, said school spokesman Brian J. Porter, "wouldn't solve all our problems, because other districts will be higher, but it's fairly competitive. It's a good, good step forward."

No figures on the cost of the entire package were available, but officials said the 6 percent increase next year would cost more than $12 million.

Fairfax County now offers starting teachers the highest salary in the area -- $18,771 -- and negotiations are under way that could result in a base wage of $20,000.