Mexico has reached agreement with 530 banks around the world on a new $5-billion loan, with $433 million being made available today as a bridge loan, Citibank and Bank of America announced in New York yesterday.

The new loan should be enough to carry Mexico through 1983, Jose Angel Gurria, the director general of credit at the Mexican finance ministry, said. Citibank and Bank of America, the largest in the United States, are among lead banks in the arrangement.

Mexico and the private banks will now have to work on the complex negotiations for a stretch-out of the nation's outstanding loans. Mexico's total foreign debt is about $85 billion, but not all of that comes due soon.

The $5-billion loan for Mexico should be signed next week, Citibank said. The financially strapped nation will probably be able to draw $1.7 billion, the first part of the six-year loan, in the middle of March, according to yesterday's announcement. The rest will be paid out in three stages before the end of the year.

The International Monetary Fund has signed a three-year loan agreement for $3.9 billion with Mexico, and IMF Managing Director Jacques de Larosiere told commercial bankers that they must also agree to put up $5 billion to help Mexico over its balance-of-payments gap. The figure was agreed to in principle a while ago, but it has taken longer than expected to reach the total.

Mexico is heavily dependent on its oil exports to obtain needed foreign exchange, and many analysts fear that falling oil prices will jeopardize the nation's economic plans and force it to ask for more money.

Gurria said that Mexico hopes interest rates will come down further as a result of the oil price decline, and that this, together with faster growth in the industrialized world, will help to offset the loss from cheaper oil. "Clearly the behavior of interest rates is very important," he said.

Mexico saves about $700 million a year for every 1 percentage point decline in interest rates, he said. It loses $550 million for every $1-a-barrel decline in the price of oil.

William Rhodes, senior vice president of Citibank, hailed the successful completion of the long, drawn-out negotiations between Mexico and its private bank creditors as "an indication of confidence by the international banking community in Mexico's ability to surmount its current economic problems."

He added that "it also is still another example of how the international financial system is responding positively to current international debt service problems."

Mexico was the first large Third World borrower to go to the banks and the IMF for help in the current debt crisis. It has since been followed by Argentina and Brazil. In all cases, the IMF has tried to push commercial banks to agree to put up new money before it has gone ahead with formal approval of the loans it has negotiated with the nations.

Mexico was lucky to be first in line, according to banking sources. Private banks, particularly small and regional banks, have become much less willing to come up with cash as the line of borrowers asking for help has grown, sources say.

However, top Brazilian officials flew to New York yesterday to sign contracts for two parts of the complicated four-part loan agreement that nation is negotiating with private banks. There were rumors in banking circles that Brazil may get an additional $500 million from the U.S. Treasury, although no such deal has yet been reached, other sources said.

Mexico and the group of banks leading the negotiations wanted all 530 private banks around the world to participate in the new loan as part of the principle of "burden sharing," whereby all the commercial banks with money already in Mexico were asked to put up some of the new money it needs, Gurria said.

One condition of the agreement was that private borrowers should resume paying interest on their debts, which had been suspended last August. Negotiations are under way to convert at least some of the unpaid interest into medium-term loans, Gurria said.