Declaring that it causes more death, disease and disability than any other illness, former HEW Secretary Joseph A. Califano Jr. yesterday called addiction to drugs and alcohol "America's number one health problem."

At the end of an 18-month study commissioned by New York Gov. Hugh L. Carey, Califano, who served as special counselor on drug abuse and alcoholism to New York state, recommended that the federal government get more involved in narcotics enforcement to reduce the flow of drugs, that it raise taxes on alcohol to discourage its use and that it incorporate research on addiction into one section of the National Institutes of Health to focus attention on it and speed cures.

"Research on addiction deserves the same kind of commitment as the federal government has given cancer," Califano said. "This is a national problem and only the federal government has the financial resources and the ability to coordinate a comprehensive research effort."

Califano put the cost of addiction in health care and lost work days at more than $100 billion a year. He said half a million Americans are addicted to heroin, more than a million abuse hypnotics and tranquilizers, several million use marijuana and cocaine regularly and 13 million abuse alcohol or are addicted to it.

"Addiction sends thousands of Americans to hospitals each day," Califano said. "It fills our jails and the crime it spawns terrorizes our citizens and destroys neighborhoods."

Of all the drugs that Americans abuse, Califano said, heroin is the most terrifying. In the last three years in New York City alone, he said, "every indicator of heroin abuse is up."

These include arrests, the number of emergency room admissions, heroin-related robbery and burglary reports and detoxification admissions. Overdoses were up more than 50 percent and overdose deaths almost 80 percent in the same period.

"There's good reason to conclude," Califano said, "that by 1981 the number of active users was as much as 50 percent higher than it was in 1978." Califano called New York City the "heroin capital of the United States."

Califano said he was making public for the first time the results of a Rand Corp. study that confirm "what most cops on the street have suspected and what our people and politicians must face:" that heroin addicts commit more crimes than other criminals to support their more than $50-a-day habits.

The Rand study found that California prison inmates addicted to heroin had committed six times as many robberies, 10 times as many burglaries and four times as many thefts and assaults as non-addicted inmates. Califano said the Rand study showed the same patterns among inmates of prisons in Texas and Michigan.

As terrifying as heroin addiction is, Califano said it is exceeded in impact on American citizens by alcoholism. He said alcohol abuse is involved in more than 66 percent of the nation's homicides, 50 percent of its rapes, up to 70 percent of its assaults and 80 percent of its suicides.

"We all pick up the tab for the three martini lunch and the tab is $60 billion for our nation," Califano said. "Only heart and vascular disease exceed alcoholism and alcohol misuse in total economic cost for the nation. Cancer and respiratory illnesses involve less than one half the economic costs associated with alcoholism and alcohol misuse."