The military would be given broad new powers to stop, search and arrest suspected drug smugglers anywhere on the world's seas under an amendment scheduled for a House vote this week.

Rep. Charles E. Bennett (D-Fla.), chairman of the House Armed Services subcommittee that deals with seapower, is sponsoring the amendment. His son died from a drug overdose in 1977.

"I don't want to waste my pain," Bennett said.

Defense Secretary Caspar W. Weinberger said that although he, too, favors eradicating drug traffic he thinks that the amendment would break down "the historic separation between military and civilian spheres of activity," which he said is "one of the most fundamental principles of American democracy. We strongly oppose the extension of civilian police powers to our military forces."

Some Defense Department officials went beyond Weinberger's legalistic arguments in explaining the Reagan administration's opposition to the amendment. One warned, for example, that the armed services could use the cover of drug interdiction to engage in unauthorized military actions in such trouble spots as Cuba and Nicaragua.

Bennett dismissed these concerns of civilian defense executives, emphasizing that the military could not move without a go-ahead from civilian agencies.

The heart of his amendment states:

"The secretary of defense, upon request from the head of a federal agency with jurisdiction to enforce the Controlled Substances Act or the Controlled Substances Import and Export Act, may assign members of the armed forces under the secretary's jurisdiction to assist drug enforcement officials of such agency in drug searches, seizures or arrests outside the land area of the United States . . . ."

Despite Defense Department objections, House vote-counters predict that the Bennett amendment will pass, partly because no extensive opposition has been mobilized.

Emotion generated by Bennett's sponsorship and frustration about the flow of drugs into the United States are giving impetus to the amendment to push the military into a new role.

Currently, a Navy destroyer that spots a suspected dope smuggler at sea or an Air Force surveillance plane that detects a suspicious light plane winging toward Florida may only warn the Coast Guard or civilian drug agencies empowered to search and make arrests.

Under the amendment, a Navy ship, for example, could be asked to stop and search a suspicious-looking craft, arrest its crew and escort the vessel to port.

Presumably, the Navy could sink a vessel that ignores warnings to stop for search.

The amendment states that such anti-drug actions by the military must not impair "military preparedness" and may be undertaken only after the attorney general determines that military help is essential and that "federal drug enforcement officials maintain ultimate control over the activities and direction of any drug enforcement operation."

Bennett recalled fury he felt when he paid a drug dealer $100 owed by his son for fear that the dealer would have his son killed if he did not pay.

"There's hardly any limit to what I would impose on the big operators who would destroy America in making wealth for themselves," Bennett said.

Weinberger, in a letter to House Armed Services Committee Chairman Les Aspin (D-Wis.) opposing the amendment, said "reliance on military forces to accomplish civilian tasks is detrimental to both military readiness and the democratic process."

"Drug smuggling," he wrote, "is traditionally a criminal enterprise" requiring "sophisticated use of informants, profiles and trained interrogators," capabilities "uniquely within the competence of civilian agencies."

Imposing drug interdiction on the military "would diminish significantly the funds and time" available to train the armed forces for warfare, he added.

"The proper role for our armed forces is to provide support so that the civilian law enforcement agencies can make necessary arrests, searches and seizures," Weinberger wrote.

The secretary noted that the Air Force and Navy conducted 10,000 hours of aerial surveillance for civilian drug enforcement agencies and loaned them $88 million in equipment last year.

The Defense Department is also concerned that the amendment would result in officers and sailors being tied up in civilian courts as witnesses rather than performing their jobs on ships.