The parent companies of New York's two largest banks reported big earning gains for the first quarter of 1979.

Citicorp, which owns New York's giant Citibank, said today that it earned $125.3 million ($1.01 a share), up 18 percent from $106.3 million (86 cents) in the first quarter of 1978.

Chase Manhattan Corp., whose earnings have been depressed in recent years because of bad loans, reported a 78 percent gain in first-quarter earnings to $71.2 million ($2.06 a share) from $41.1 million ($1.21) for the first quarter of 1978.

Chase Manhattan Chairman David Rockefeller said that the first-quarter performance demonstrates that the bank's efforts to upgrade its loan portfolio that began several years ago "have begun to pay off."

"And while we are still not content with either the level of our earnings or our earnings or our performance in such key areas as return on assets and shareholders equity-as first-quarter results suggest-we are definitely moving in the right direction," Rockefeller said.

Both big bank holding companies released their first-quarter results at their annual shareholder meetings.

Citicorp Chairman Walter W. Wriston, under shareholder questioning, denied that the bank owes large sums in taxes to foreign countries as a result of allegedly illegal transfers of foreign exchange profits from countries in which they were earned to the Bahamas.

A former Citibank foreign exchange David Edwards, charged publicly last year that Citibank employes regularly "parked" foreign exchange profits in the Bahamas. Edwards has been fired by the bank and is suing the company.

Wriston said that an eight-month investigation of Edwards' charges by the bank's auditors, Peat, Marwick and Mitchell, and the law firm of Shearman and Sterling found "no pattern of the violation" alleged by Edwards, although the reports did discover "some transactions that could be questioned."

Wriston told professional shareholder Evelyn Y. Davis that the bank is "talking to some governments" but that "no tax claim has been asserted so far."

He denied that Edwards was fired after he made the allegations, although Edwards has claimed that he complained about the allegedly illegal transactions for more than a year to bank officials and made the charges public only after Citibank fired him.

Wriston also said that the bank's board of directors have considered its lending policies to utilities using nuclear plants, but decided that the bank should not change its policies despite the nuclear accident at Three Mile Island near Harrisburg, Pa., late last month.

He said Citibank does business with all 24 utilities that operate nuclear plants, but said the loans are to the utilities themselves and in no way are dependent upon the operation of the nuclear facilities.

Shareholders turned down a proposal to require the bank to detail its commitment to South Africa as well as a resolution to force the bank to curtail its lending to chile.

Howard Schomer, who controlled proxies for 5,000 shares of Citicorp's stock owned by the United Church Board for World Ministries, said that his church was closing its commercial account and 29 trust funds at Citibank "through which we have long handled the business aspect of our $7 million annual program."

Schomer's organization was a strong backer of the resolution to require the bank to detail its lending to South Africa because of that country's apartheid policies.

Wriston said that, while the bank found apartheid repugnant, there were severe differences of opinion over whether the black majority in South Africa is hurt or helped by U.S. bank lending and corporate investments in the country.

Citibank has made no loans to the South African governments in the last two years.

Wriston said that the strong first-quarter earnings occurred dispite a slowdown in foreign exchange profits.

The bank said that the return on shareholders' equity was 15.6 percent (at an annual rate) in the first quarter compared with 14.7 pecent last year while the return on average total assets was the same, 0.58 percent.

The bank's total assets were $91.5 billion on March 31 compared with $79.1 billion the year before. Total loans rose to $53.3 billion from $46.8 billion, while deposits increased to $62.6 billion from $57.6 billion.

Chase Manhattan said the return on its assets of $58.1 billion average 0.51 percent in the first quarter, up from a return of 0.32 percent on $52.7 billion in assets in the first quarter of 1978.

Chase had loans of $36.2 billion in the first quarter compared with $32.6 billion a year before, and deposits of $44.3 billion compared with $40.8 billion in the first quarter of 1978.

Rockefeller said the bank expects continued improvement in performance during 1979, although he admitted to shareholders that the "economic environment in which we will operate this year appears to be getting more cloudy."

He said the "best we can expect in 1979, I'm afraid, is for relatively modest economic growth. There is a real possibility that we would have no growth-or even slightly negative growth-this year. Obviously, no U.S. economic growth. There is a real possibility that we would have no growth-or even slightly negative growth-this year. Obviously, no U.S. economic forecast at this moment can be made with absolute assurance."

But unless there is a significant disruption of oil supplies, conditions do not exist for a serious economic slide of the type the country experienced in 1974 and 1975, Rockefeller said.

He said business is so "robust" today that demand for money can be expected to remain strong and interest rates high for some time to come.

Bankers Trust New York Corp. reported a 53 percent gain in profit for the first quarter to $2.20 a share from $1.44 a year ago. Net income rose to $26.9 million from $19.7 million.

Chairman Alfred Brittain III said larter trust fee volume and better net interest margins produced the gains. In addition, the loan loss provisions declined.

Manufacturers Hanover Trust Co., parent of the nation's fourth-largest bank, reported first-quarter net income of $51 million (1.56 a share) compared with $43.5 million ($1.34) in the 1978 first quarter.

Results included $66,000 in securities losses against securities gains of $216,000 a year earlier, and a foreign exchange translation loss of $331,000 against a gain of $612,000 a year earlier.

Continental Illinois Corp., parent of the Continental Illinois Bank, the nations seventh-largest, had a 16.7 percent gain in net income for the first quarter to $46.36 million ($1.19 a share) from $40.13 million ($1.12) a year ago.

Chairman Roger M. Anderson said net interest income rose 22.1 percent and total average loans outstanding increased 24.7 percent from a year ago to $18.3 billion. CAPTION: Picture, Chase Manhattan Corp. Chairman David Rockefeller, behind lectern, addresses stockholders in New york yesterday. AP