Talks between the government and representatives of the air traffic controllers' union aimed at reaching agreement on a new contract broke off yesterday, increasing the possibility of a strike next Monday that could affect most of the nation's air service.

At a news conference yesterday afternoon, Transportation Secretary Drew Lewis and FAA Administrator J. Lynn Helms said that Robert E. Poli, president of the Professional Air Traffic Controllers Organization, had walked out of a morning meeting after rejecting a government proposal that would have given the controllers additional wages and benefits costing $40 million a year.

Although he was not available for comment yesterday, Poli has said in the past that if no acceptable settlement proposal is in union hands by 11:59 p.m. June 21, a decision to strike could affect the 7 a.m. shift on June 22, despite a continuing injunction barring a PATCO strike.

Declaring that there is "no justification . . . whatsoever" for PATCO's demands, which he said would cost the government $1.1 billion a year, Lewis warned yesterday that controllers who don't show up for work will be subject to criminal prosecution. "The administration is going to take a very strong stand," he said. "We are not going to tolerate an illegal strike."

In the event of a walkout, the government is prepared to implement an emergency plan which is expected to halt at least half of U.S. commerical air traffic. Under the plan, transcontinental and international flights essentially would be unaffected while virtually all flights of under 500 miles would be grounded. A controllers walkout, which the airline industry estimates could cost the airlines about $80 million a day, would severly disrupt air travel at the busiest travel season of the year.

If a walkout is complete, Lewis and Helms estimated that the FAA could handle up to 27 percent of the nation's flights with FAA supervisory personnel. But both expressed confidence that some union members would continue to work if there is a strike. "[Not] all of our controllers are . . . even members of the union," Helms said. "I happen to believe that not anywhere near all of them will go out."

About 14,800 of the nation's 17,000 controllers are PATCO members. Their contract expired March 15. The union has demanded a minimum salary increase of $10,000, a reduced work week from 40 to 32 hours, an improved pension plan and other benefits.

The FAA proposal rejected by PATCO yesterday was characterized by Lewis as "fair and comprehensive." It offered:

A 10-percent pay raise for controllers who act as on-the-job training instructors, and an increase in pay for night duty. Under the proposal, controllers would receive a 20 percent pay differential for working at night instead of the current 10 percent differential.

A guaranteed half-hour lunch period, or the equivalent in overtime pay, per eight-hour shift.That would mean in effect paying controllers who work 37 1/2 hours a week for a 40-hour week -- representing about a 6 percent reduction in the total hours worked.

An assurance that the 11,500 controllers assigned to the nation's busiest towers and centers would spend no more that 6 1/2 hours at an operating position.

Payment of one year's salary as severance pay to any controller with five years' consecutive service at a high-traffic facility who is disqualified from service for medical reasons. Controllers now can retire after 25 years' service or, at age 50, with 20 years' service.

An opportunity for PATCO members to join advisory committees concerned with possible changes in FAA controller procedures.

Lewis noted that air traffic controllers are "among the best-paid employees" in the Federal Government earning more than $37,800 a year after five years, not including overtime and other compensation. "On that basis, a controller now can earn as much as $50,112 plus overtime, which is the maximum salary currently allowed for a federal career employe," he said.

"We feel we've offered a fair package, the maximum that we can justify in terms of the economic conditions of the country at the present time and in terms of what they deserve to get paid and what the taxpayers can afford to pay them," Lewis said. Although the administration won't alter the price of the total package, he said they are prepared to "move individual items around" if PATCO desires.