Abortion opponents have launched a new attack on Thomas R. Burke, chief of staff of the Department of Health and Human Services, charging him with an "insidious" effort to wrest the government's teen-age pregnancy program from an abortion foe.

"Family Protection Report," published by conservative leader Paul Weyrich, has charged that Burke orchestrated an unsuccessful plan to take the $14 million teen-pregnancy research program from Jo Ann Gasper, deputy assistant secretary for population affairs, and shift it to another HHS agency, the Family Support Administration, headed by Wayne Stanton. FSA administers the welfare program for mothers with dependent children.

Weyrich, president of the Free Congress Research and Education Foundation, did not write the report but said he endorses it.

The June issue said Burke sought to strike out at Gasper because she tried earlier this year to ban Planned Parenthood from the government's Family Planning Program, which Gasper also supervises.

In the Planned Parenthood dispute, Gasper found that the group's general advocacy of abortion outside the Family Planning Program made it unsuited to participate in a government project. She did not charge that the organization had used Family Planning Act money to advocate or perform abortions, which is forbidden by law.

Gasper's effort to exclude Planned Parenthood was rescinded after Burke and other HHS officials were advised by department lawyers that such action was illegal.

Burke has told associates that allegations he is seeking to "punish" or "ruin" Gasper for her antiabortion views are false; that as a Roman Catholic, he strongly opposes abortion, and that he proposed that Stanton undertake an anti-teen-pregnancy program before he learned Gasper was running one.

Neither Burke nor Gasper could be reached for comment.

The new criticism of Burke is the latest step in a sharp conservative campaign against him, which began with HHS Secretary Otis R. Bowen's plan to add catastrophic-illness insurance for the aged to Medicare. Conservatives disliked the idea of enlarging a government program and preferred to have protection against catastrophic illness provided through private industry. They blamed Burke, who helped Bowen develop the plan, for advocating use of the Medicare program.

Burke drew added conservative fire as a key figure in rescinding Gasper's order to ban Planned Parenthood from the government's Family Planning Program. Under that program, the government finances family-planning clinics with grants to various groups. Officials are forbidden to use grant money to advocate or perform abortions, but the law has never been interpreted as barring a grantee from using money from other sources to perform or advocate abortions.

Abortion foes have long sought to impose the rule that any group that performs or advocates abortion, even if only with its nonfederal money, be barred from the program. They were furious when the department failed to adopt such a rule, and Weyrich called for Burke's ouster.

The latest flap began when Burke, after reading a newspaper article about a private program to deal with teen-age pregnancy, concluded that it would be a good idea to let Stanton's FSA make grants to private groups for various activities mentioned in the article.

At the time, Burke told associates, he did not know that a teen-pregnancy program, authorized in 1981 through efforts of then-Sen. Jeremiah Denton (R-Ala.) and Sens. Edward M. Kennedy (D-Mass.) and Orrin G. Hatch (R-Utah), existed and had $14 million in 1987 for grants to local public, private and religious groups for demonstration projects. The projects included programs to encourage adolescents to postpone sexual activity and grants to provide care services or pregnancy-prevention services.

When Burke learned of the program, which was under Gasper's supervision, he decided it should be transferred to Stanton's FSA.

However, Anthony McCann, assistant secretary for management and budget, reported to Burke that the law appeared to require that the teen-pregnancy program be under the general jurisdiction of the assistant secretary for health -- Gasper's boss -- and that the deputy assistant secretary for population -- Gasper -- administer it.

Burke then encouraged an alternative plan to allow Stanton's office to help review grant proposal notices before they appear in the government's Federal Register. He also backed the idea of a Stanton representative sitting in on "all grant review panels which select grantees."

Bowen never approved this plan. The latest word is that while no formal sharing of jurisdiction will be arranged, "informal coordination" between Gasper and Stanton will be urged.

The teen program, meanwhile, has run into legal trouble. On April 15, U.S. District Court Judge Charles R. Richey ruled that portions of the law permitting grants to religious institutions were unconstitutional and had permitted use of federal funds "to educate or counsel on matters inseparable from religious dogma."