Two pilots attempting landings in Los Angeles and Chicago reported to the Federal Aviation Administration yesterday they had to make sudden, sharp turns to avoid colliding with small private planes.

The incidents were the fourth and fifth since Saturday in which jet pilots avoided midair collisions by only a few hundred feet. In four of the incidents, the pilots had to swerve sharply to avoid colliding. Four of the incidents involved small planes.

After the Los Angeles incident, FAA chief Allan McArtor announced yesterday he is placing more limits on private plane traffic around Los Angeles.

In that incident, an American Airlines pilot was forced to bank sharply to the left and dive to avoid hitting a small, unidentified private plane as the American jetliner approached Los Angeles International Airport. The encounter took place Tuesday evening at 7,400 feet just outside the boundary of the restricted airspace that prohibits private planes from entering without permission and electronic altitude reporting devices.

FAA officials estimated the two planes passed within 300 feet of each other.

In his announcement, McArtor said he is enlarging the restricted airspace and closing a north-south corridor over the Los Angeles airport through which small planes can fly. The FAA had announced plans to make the changes last week, but after Tuesday's incident, McArtor said they will take effect next Wednesday.

McArtor said he was taking the action to "lessen the risk posed to the traveling public by VFR {visual flight rules} aircraft in and around the Los Angeles basin."

Nearly a third of the country's general aviation aircraft are registered in California, according to a spokesman for American Airlines.

The number of reports of near-collisions is up 31 percent over last year, an increase attributed by aviation experts to a combination of both an increase in the number of incidents and an increase in the number of reports made to the FAA.

In the first seven months of this year, the FAA reports, there have been 150 near-collisions involving at least one jet airliner. That compares to 82 reports of near-collisions involving at least one jetliner in the first seven months of 1986.

Overall, in the first seven months of this year, 610 near-collisions have been reported to the FAA, compared to 464 reports of near-collisions made in the first seven months of 1986.

The rise in near-collisions, particularly the daily occurrences since Saturday, has renewed the call by the aviation industry to more swiftly require all small planes flying around busy airports to be equipped with altitude reporting devices. The FAA is requiring small planes flying around the nation's 23 busiest airports to be equipped with the devices, known as Mode-C transponders, by Dec. 1.

"These incidents also highlight the need for modernization of the entire air traffic control system, which is still operating with outdated computers and too few controllers," said William F. Bolger, president of the Air Transport Association, the lobbying organization for the nation's major airlines.

In the Los Angeles incident, the American plane, a Boeing 737, was carrying 78 passengers and four crew members on a flight from Seattle and San Francisco. Passengers interviewed by The Associated Press after the plane landed in Los Angeles said they were startled by the jetliner's sudden lurch.

"I was petrified," said Cathy Kartow of Anaheim, Calif. "I don't know if I will fly again."

The Chicago incident involved a corporate Lear jet and an unidentified private plane as the jet was approaching Midway Airport for a landing.

The Lear jet's pilot, who dove suddenly to avoid hitting the plane, told the FAA: "I was so close I could read his number," said Mort Edelstein, an FAA spokesman.

Edelstein said the Lear jet, owned by the Fort Howard Paper Co. of Green Bay, Wis., was about 1,000 feet from the runway, under direction of air traffic controllers when he saw a single-engine Piper Cherokee "almost upon him," Edelstein said. Printouts of radar showed the two planes were separated by 500 feet.

"The Lear jet pilot told the tower that he had to dive, he had to go down, quick down," Edelstein said. A controller at Midway radioed the Piper pilot in an attempt to avoid a collision, but got no response, Edelstein said.

Edelstein said the Lear jet seats eight with a crew of two and the Piper seats four with a crew of two.

The incidents came one day after a near-collision in Dallas. In that case, a Delta Air Lines pilot flying a Boeing 727 carrying 104 people, was forced to turn sharply to avoid hitting a small plane in its path as it approached Dallas-Fort Worth International Airport about 12:30 p.m. Monday.

Last Saturday, an Air Canada jetliner had just departed Chicago's O'Hare International Airport when a twin-engine Cessna plane passed within about 300 feet.

On Sunday, a Pan American Airways jetliner approaching LaGuardia Airport in New York for a landing was forced to dive to avoid hitting a Trans World Airways jet that had flown into its path as it approached John F. Kennedy International Airport for a landing.

Both weekend incidents were attributed to controller errors, FAA spokesmen said.