Nearly 80 percent of Argentina's 310 big bank lenders, including almost all its British bankers, have approved a new $1.5 billion medium-term loan for that nation, Citibank Senior Vice President William R. Rhodes said yesterday.

Rhodes also said the final $300 million installment of the $1.1 billion bridge loan key banks agreed to make Argentina to tide it over until it could arrange more permanent financing will be disbursed next week.

Rhodes said the $1.5 billion loan agreement for Argentina is "going much better" than anticipated. He said 241 banks already have signed the medium-term agreement and all but 32 have indicated they have no problem with the loan.

Rhodes--who heads up bank committees involved in restructuring debts for Mexico, Brazil, Peru and Uruguay in addition to Argentina--said the first portion of the new medium-term loan will not be disbursed to Argentina until at least the middle of September.

By then, he said, banks hope to have completed the first "restructuring" of Argentinian loans that came due in 1982 and 1983 but could not be repaid on time. That restructuring agreement, for the Argentine national airline, should be signed early in September, the Citibank vice president said.

For most of the troubled Latin American borrowers, the debt negotiations have two different, but related steps. Not only must the terms on maturing loans be stretched out, new loans must be negotiated. Banks and Argentina have been working on the $1.5 billion new loan for nearly a year. Rhodes said the banks want to wait to actually disburse any of the new money until the first stretch-out agreement for an Argentinian loan was completed.

The airline loan is relatively small, Rhodes said. Eventually Argentina must reach agreement with its bankers to stretch out $6 billion worth of public-sector loans and $5 billion in loans to Argentina's private sector that came due during 1982 and 1983 but on which no principal was paid. Like all Latin American debtors Argentina has agreed to keep interest payments current, although Argentina has fallen somewhat behind on those payments as has Brazil.

A major stumbling block in the Argentinian agreement was the financial sanctions that Argentina and Great Britain imposed upon each other during the Falkland-Malvinas war between those two nations. The British banks were under pressure not to sign because Argentina still refused to permit British firms operating in Argentina to repatriate dividends and profits to Britain. Last week Argentina lifted those sanctions, paving the way for British banks to sign the loan agreement.

Argentina, with between $40 billion and $45 billion of foreign debts, is the third biggest borrower in Latin America, behind Brazil and Mexico.