Johnson & Johnson Co., trying to hold on to its share of the lucrative over-the-counter pain-reliever market, yesterday stepped up its public relations campaign to save the image of its top product, Tylenol.

Chairman James E. Burke went on the nationally syndicated "Donahue" show to address public concerns that have mounted ever since a New York woman died from a cyanide-laced Extra-Strength Tylenol capsule 11 days ago. One other bottle of cyanide-laced Tylenol was found in another store near where the first bottle had been sold.

At the same time, full-page advertisements were placed in New York newspapers offering to replace or refund consumers for any Tylenol capsules they have. The replacements will be "caplets," elongated, coated tablets that the company began making several years ago in an effort to come up with a more tamper-resistant drug. Johnson & Johnson said earlier this week that it will no longer make capsules for over-the-counter medications.

Burke also continued to openly discuss the latest developments, holding a news conference after attending a long-scheduled White House meeting with 100 executives of the Business Council. At that meeting, President Reagan congratulated Burke for living "up to the very highest ideals of corporate responsibility and grace under pressure."

Although Burke said law-enforcement officials still did not know how the poison was placed in the bottles they showed no signs of being tampered with , he said he remained convinced that the tampering did not take place in the company's factories or warehouses.

"It is really based purely on mathematical probability, nothing else," Burke said. Tracing the manufacturing and distribution of these two bottles, made at different times and places, is mathematically impossible, he said.

Nonetheless, he added, "I'm not so sure it would be all bad if it was found to have happened in our factory or our warehouse. It would limit very sharply the number of people that could have tampered with the containers . We would have a much better chance of finding out who the perpetrator was. I personally think that the consumer would not only be relieved, but would forgive us, because whoever did this was mentally deranged."

Burke declined to criticize the decision by other manufacturers to continue making capsules However, he noted, his company has concluded that some of the more sophisticated products other companies are now touting are not tamper-proof.

One method involves electronically sealing the halves of the capsules to make it difficult to tear them apart without the capsule breaking. Johnson & Johnson experts found that while most sealed capsules would break, it was still possible to open about 5 percent of them, Burke said. "Nothing is 100-percent tamper-proof. Nothing is 100-percent fool-proof," not even the caplets, he acknowledged.

Burke said that, in retrospect, he regretted the company's decision to continue sales of Tylenol capsules in 1982, after seven people died in Illinois from cyanide poisoning contained in the capsules. At the time, however, he said the company felt its tamper-resistant seals on the bottles were sufficient to avoid a repeat incident.