Census Bureau director Vincent P. Barabba yesterday disputed charges that the 1980 census has seriously undercounted population in the nation's big cities.

Barabba, beset by lawsuits from New York, Detroit and other jurisdictions, said it now appears that the actual count of people residing in the United States on Census Day -- April 1, 1980 -- will turn out to be 225 million to 226 million, about 4 million persons more than the bureau thought it would find.

Barabba made clear that he believes the exta people have turned up because of improved counting techniques.

It is conceivable, he said, that there is a "zero undercount" but this is probably far too optimistic an assumption because some illegal immigrants probably have been missed.

Barabba's assertion that the count is "by far the most complete census in our history" came as public officials in northern cities continued to press claims that the Census Bureau is missing substantial blocks of the population, particularly minorities, in their jurisdictions, threatening them with a loss of congressional and state legislature seats and federal grants, all of which are based on population.

Barabba's worst problems are in Detroit and New York. A federal judge in Detroit, responding to a suit by the city, ruled that the Census Bureau may not publish the results of the 1980 census until it finds some accurate method to estimate how many people it has missed in each state, city, county and even election district and adjusts all the figures upward. Barabba claims this can't be done in time to report overall state figures to the president by Dec. 31 and political subdivision figures to the states by April 1, as required for reapportionment.

Census officials told the judge that the undercount isn't nearly as great as many claim, but last Thursday he rejected their arguments and gave them two weeks to come up with an estimating method.

New York City is demanding census records to check the count. Barraba says this violates promises of confidentiality to citizens, widely publicized in TV spots by such persons as Rosalynn Carter, boxer Sugar Ray Leonard and football stars Roger Staubach and Efren Herrera.