A long dispute between Israel's doctors and the government deepened today as most doctors walked off their jobs at public hospitals and the Cabinet authorized the issuance Monday of legally binding back-to-work orders.

The almost three-month-long, increasingly bitter dispute between the doctors and the government has already reduced the level of health services in Israel and is part of a broader pattern of mounting economic problems afflicting the country. Inflation in April was the highest ever for a single month, and the country also is heading for a record deficit in its balance of payments.

The central issue in the doctors' dispute is their demand that they be granted salary increases substantially larger than the 22 percent pay raise the government approved for most other public employes last fall. Earlier, the doctors responded to the government's rejection of their salary demands by closing publicly supported clinics, reducing the number of physicians working at public hospitals and charging patients about $15 for visits to private clinics they hastily established to provide medical care.

Today's action by the doctors left most hospitals in Israel staffed with 10 percent or less of the normal number of doctors. The Tel Aviv municipal hospital normally has a staff of 400 doctors, but today only about 10 physicians were said to be on duty there.

Despite the seriousness of the situation, today's developments had an almost comic overtone. Doctors, given secret instructions in sealed envelopes, were spirited off to undisclosed locations in chartered buses to avoid being served with the anticipated back-to-work orders.

At one point today, the interior minister, Yosef Burg, ordered Israel's southern border crossing with Egypt at Taba closed to prevent doctors from fleeing into the Sinai Peninsula. But the tourism minister, Avraham Sharir, complained about the order and the border crossing was later reopened.

Most medicine practiced in Israel is publicly supported and Israelis who belong to labor unions or other public sick funds are provided free health care in the public clinics and hospitals. Although some doctors have private practices, the vast majority work in the clinics and hospitals and are paid negotiated salaries regulated by the government.

The key figure in the dispute with the doctors is Finance Minister Yoram Aridor. With the transfer of Ariel Sharon from the Defense Ministry to a powerless post as minister without portfolio, and the country growing more concerned about domestic economic issues, Aridor has become probably the single most controversial figure in the government of Prime Minister Menachem Begin.

The doctors' action today added to Aridor's problems. It came a week after the announcement that Israel had registered the highest rate of inflation in a single month in its history, a 13.3 percent jump in prices in April.

Inflation in Israel last year was 131 percent, the second highest annual rate in history. For the first four months of this year, inflation has been running at a 160 percent annual rate.

Moreover, Israel's projected balance of payments deficit this year is a record $4.9 billion. This led to a meeting last week between Begin and representatives of the Israel Manufacturers Association who complained about Aridor's economic policies and whose president recently was quoted as calling the finance minister "infantile and irresponsible."

But Begin has shown no public signs of wavering in his support for Aridor, who is widely credited with making a major contribution to the prime minister's reelection victory in 1981.

Aridor took over the Finance Ministry in January of that year with Begin's Likud Bloc government at a low ebb in public opinion polls. He immediately slashed taxes on consumer goods and pumped money into the economy, setting off a consumer spending spree that helped lift Begin's political fortunes before the election.

But critics of Aridor charge the price of these tactics is the triple digit inflation that continues to plague the country and that Aridor and Begin pledged to curb. The government has embarked on an anti-inflation campaign, including changes in Israel's generous cost of living allowance payments that cushion the effects of inflation and that were negotiated last year with the Histadrut, the country's giant labor federation.

Aridor has taken an extremely tough line against the doctors' salary demands in part because he fears a revolt from the unions that belong to the Histadrut if the doctors are granted more than the 22 percent increase the other unions agreed to accept last year.

There were no reports today of serious medical incidents growing out of the doctors' action. This has been true throughout the dispute as Israelis have learned to cope with the latest episode in the country's strife-ridden labor relations.

But the walkout from the public hospitals was a sharp escalation in the confrontation and some hospital officials were quoted as saying the situation at their facilities was near "collapse."

Israeli radio tonight reported appeals for a quick settlement of the dispute by Chaim Herzog, Israel's newly installed president, and the country's two chief rabbis. But spokesmen for the doctors vowed that they would not return to work and Attorney General Yitzhak Zamir said he would prosecute any doctor who defied the back-to-work orders.