Responding to critism that standards have fallen in American schools, Mary F. Berry, the Carter administration's top education official, suggested yesterday that the federal government should try to develop national tests in reading, writing and mathematics that schools could use to judge student performance and try to improve it.

Berry, who is assistant secretary for education in the Department of Health, Education and Welfare, told a Senate subcommittee that she opposed proposals for establishing national standards of minimum competency in basic subjects. But she said a national yardstick in these subjects - which does not exist now - would be a good idea.

"That way a school district could see how its ninth graders stack up with other ninth graders around the country," she said in an interview later. "Then the district could decide what scores it wants to expect from the students."

"There may come a time," she added. "When we (in the federal government) can make a judgement of what a nationally imposed standard should be, but at this time we don't know."

Berry also cautioned that it must be left up to local school districts to decide whether they want to give federal sponsored tests.

Earlier in the hearing before the Senate education subcommittee, Adm. Hyman G. Rickover, head of the Navy's nuclear ship program and a long-time critic of American education, urged that the federal government establish a formal system of tests at different grade levels and in most major academic subjects to see whether students can meet minimum competency requirements.

Rickover said that although states and school districts would have to decide whether to give the tests, any parent should be able to have his child take them at government expense.

Without national standards, Rickover said, high school diplomas have been cheapened so much that in many cases they are a "fraud."

"Parents and students must accept the unpleasant fact that today's awards and diplomas do not necessarily imply academic achievement," he declared. "Grade inflation, far from helping students, (has) robbed them of a proper education; too late they discover how little they really learned. Accepting a diploma without an education makes no more sense than getting vaccinated and not finding out if the vaccination took."

Sen. Claiborne Pell (D-R.I.), the subcommitee chairman who conducted hearing, endorsed Rickover's idea of national competency exams, but said they should be limited at first to reading, writing and mathematics because these are the subjects on which a national consensus exists about what students should know.

Pell said Berry's support for national tests without competency standards did not go as far as he would like, but he praised it as a "good step forward."

Since 1970 the federal government has sponsored a National Assessment of Educational Progress, which tests children at several ages as well as young adults. But because if opposition from major groups of teachers and school administrators, the tests are not connected to grade levels in school or to graduation from high schools.

Also, the assessment tests set no standard of what children should know, and are given only a sample basis around the country, so that individual children, schools, and districts cannot be compared to national averages.

Several publishing companies also sell standardized tests with comparisame tests nationwide.

But Berry said the norms on the different tests are substantially different and there is great controversy about how valid they are. She said the first step in developing federal tests should be to study and evaluate for the National Institute of Education the existing private tests and give advice to school districts about which ours are best.