The group that represents Montgomery County teachers has spurned an offer from school officials to raise the starting salary of beginning teachers by almost $3,000 a year, leaving school officials stunned and angered yesterday.

The Montgomery Board of Education, expressing concerns that Montgomery may not be competitive with other local jurisdictions in salaries when recruiting new teachers, made the offer this week to the Montgomery County Education Association, the bargaining unit that represents the county's 6,200 teachers.

The proposal would have increased the starting salary level next year from $17,187 to $20,000, a 16 percent raise. But union approval was required because teachers' salaries are set in a contract that does not expire until the summer of 1987.

Union officials said they turned down the offer because it would benefit only the teachers in the lower salary ranges, about half the teachers in the system.

School board member Sharon DiFonzo said yesterday, "I'm flabbergasted that they turned us down. It's a freebie. It's a gift. It doesn't cost them anything and we're not asking for anything in return."

Blair Ewing, another member of the board, said he too was "astounded" by the rejection. "Unless we can change this somehow, we're in a situation where we will lose good teachers and it will be their fault."

Board members said they were hoping the pay increase would help them hire about 850 new teachers that will be needed next year.

Alexandria, Fairfax County and Arlington County are considering proposals that would raise the starting annual pay of teachers next year to about $20,000.

Under the board's proposal, which school officials said would cost $2.7 million, teachers at several other steps in the pay scale above the starting salary would receive small pay raises, but beginning teachers would receive the heftiest increase.

Mark Simon, president of the Montgomery County Education Association, said his group objects to a proposal that benefits only one group of teachers.

"The offer is unfair, divisive and destructive of the morale of teachers currently employed," he said.

Simon said the 16 persons who sit on his group's board of directors voted unanimously to reject the board's offer.

"Our position is very principled," he said. "Basically, the board wants to solve its problem without dealing with any of the problems and concerns that we are raising."

A recent union survey of Montgomery teachers indicated that 40 percent of those responding were seriously considering leaving the teaching profession. They cited low pay and poor working conditions, such as overcrowded classrooms and too little planning time.

Vicki Rafel, president of the Montgomery Council of Parent Teachers Associations, said her group will not take a position on the matter, although it has gone on record in support of pay raises for teachers.

"It's a labor-management dispute and I don't want either side pulling parents into it," she said.

At a news conference yesterday, Jim Cronin, president of the Board of Education, said it is unlikely the County Council would approve a 17 percent across-the-board pay raise for all teachers because it would cost $36 million.

Cronin said he hopes the teachers union will reconsider the pay offer. "The offer is still open," he said.

But Simon said that is unlikely.

"We want to start discussions on salaries, period," he said. "That's our formal position."