The Carter administration has voiced strong opposition to a House measure that would require 18 year-olds to register for possible military service starting 18 months from now.

"This administration opposes peacetime registration for the draft," White House domestic affairs adviser Stuart E. Eizenstat wrote in a letter this week to congressional critics of the legislation.

"We do not believe it is necessary to impose this burden on our nation and its youth at this time when there are effective ways to improve the capability of the Selective Service System so it can respond quickly in time of emergency," Eizenstat's letter said.

Administration witness had indicated little enthusiasm for the registration plan during hearings earlier this year. But as late as last week both supporters and opponents of the measure remained unsure of the White House and Defense Department's position.

The Joint Chiefs of Staff had come out in support of peacetime registration after the proposal was tacked into a military procurement bill earlier this year.

In the past two weeks, however, a variety of administration officicals have sent letters to the Hill -- each one stronger than the last -- reflecting at first a disinclination for peacetime registration, and finally opposition.

Shortly before Eizenstat's letter was sent Monday, Defense Secretary Harold Brown wrote Rep. Charles E. Bennett (D-Fla.), a supporter of renewed registration, a milder note saying, "i oppose peacetime registration at this point."

The registration question has been a ticklish political issue. Supporters have worked hard to contest the idea that this would be the first step toward reinstatement of the draft in place of an all-volunteer force.

The draft ended in 1973, after years of passionate opposition, much of it by antiwar activists of the Vietnam era.

The latest registration propoal is being fought by a coalition of liberals and conservatives, including 40 members of Congress and such groups as the American Civil Liberties Union and Americans for Democratic Action, as well as by the exective director of the National Taxpayers Union.

Supporters of registration have repeatedly called it "an insurance policy," But the effect of the escalating administration opposition to the bill "is devastating," Rep. Marjorie S.Holt (R-Md) said yesterday.

"The lobbying effort they'er putting forth will certainly have an effect," Holt added. The $40 billion procurement bill, with the registration provision attached, had shown considerable strenght when a key procedural vote was taken on the House floor last week.

Rep. Richard C. White (D-Tex.), one of the chief backers of registration, said yesterday that the White House opposition "looks a little strange at this stage ...We hadn't heard from the White House at all" before this he said.

The Eizenstat letter recommended that instead of reinstituting registration, the House support a proposed increase in the budget "to enchance the standby ability of the Selective Service System, including its computer resources, its staffing and its planning."