The Washington Teachers Union has called for a city mediator to get involved in its contract talks with the D.C. Board of Education, union president William H. Simons said yesterday. The talks have been stalemated for nearly seven months.

While both sides are deadlocked over several items, the two key problems are salary demands and a proposal by school board negotiators that would make teachers' work eight-hour days instead of the current 6 1/2-hour days, and add 15 more working days to their contracts.

"We have reached the point at which it would serve no useful purpose to continue face-to-face discussions," said Simons, who accused the board's negotiators of being "incompetent and intransigent" during the extended talks.

Simons said the board has refused to make a reasonable offer to his union, which represents 4,200 Washington teachers.

Kenneth Nickoles, spokesman for the school board's negotiating team, responded by charging the union with being uncooperative. "We've been ready to negotiate but all the sudden, Mr. Simons decides things are not proceeding his way and there is an impasse," Nickoles said.

The current contract was signed in 1979, following a bitter 23-day school strike. Technically, it expires Jan. 2, but will remain in effect because of the ongoing negotiations. Simons said yesterday that he saw "no danger of any job action at the present time.

This is the first year that the union has been allowed to negotiate salary demands with the board and negotiations have been bogged down several times.

Once the city's independent Public Employee Relations Board assigns a mediator, both sides will again sit down for talks. If mediation fails after 30 days, the two sides could be forced to enter into final and binding arbitration.

When talks began in June, the union sought a wage increase of 43 percent spread over the next three years. The board countered with a 10 percent salary package spread over three years.

The union's most recent demand was for an overall 22 percent, three-year salary increase which, Simons explained, is identical to what the D.C. police union recently won.

The board countered with an offer to increase salaries by 10 to 13 percent during the next three years, or an average of about 4 percent per year.

Disagreement about salaries, however, is not what made Simons ask for mediation, he said. Rather, he said, he was upset about the board negotiators' insistence that teachers work eight-hour days. It also wants teachers to work until the end of June, rather than leaving school in the middle of that month.

"It's simply quid pro quo," Nickoles explained. "All we are saying is that some type of increase in services will be required for an increase in compensation."

Washington teachers, whose salaries in 1979 averaged more than $20,000 a year, get paid for a full day of work, said Nickoles, which "should mean eight hours." Also, teachers are paid for working the entire month of June even though school ends during that month, he said.

"There is plenty that they could be doing if they stayed until July 1 ," said Nickoles, who suggested teachers could tutor students and help with school-closing chores.

Simons disagreed. "They have this asinine view that any kind of adjustment in salary means the teachers must work more time rather than taking into consideration inflation and performance," said Simons. "They've tried this for the past five years and they've lost every time. We aren't even going to bother talking about it now."

The board and union also are deadlocked over a board proposal that would require teachers to receive satisfactory job performance evaluations before they could move to a higher salary step.