Health and Human Services Secretary Margaret M. Heckler yesterday announced "substantive improvements" in a preventive health program for poor children that the Reagan administration once considered watering down.

She said the administration is implementing final regulations aimed at strengthening the Early and Periodic Screening, Diagnosis and Treatment Program, run by states with federal and state money.

The Medicaid program tests poor children for vision, hearing, dental or other health problems, including handicaps and poor nutrition. States are required to treat problems that turn up.

Children's advocacy groups and Capitol Hill Democrats praised the proposed rule last year, calling it a welcome change from a 1982 proposal by President Reagan to eliminate the list of services states must provide.

Sara Rosenbaum of the Children's Defense Fund said yesterday that she is pleased that Heckler signed the final rule, but added, "it is hardly a testament to their concern for children that they are now releasing regulations that they at first tried to destroy and now sat on for two years."

Rosenbaum said the timing of the rule's release two weeks before the election was "mighty coincidental."

The rule was approved March 15 by Carolyne K. Davis, who heads the HHS division that runs Medicaid, and who then sent it to Heckler's office. HHS officials said they did not know why it took seven months for Heckler to approve and release the rule.