The Carter administration is having problems getting NATO allies to support publicly a decision to produce and deploy a new generation of neutron weapons, according to informed U.S. officials.

Neutron warheads for the Lance missile and 8-inch artillery have become a "controversial political issue" in Europe where they would be deployed and possibly used, sources said.

The proposed neutron warheads are the first tactical nuclear weapons designed specifically to kill enemy troops primarily by radiation rather than destroying their tanks, other equipment and installations by blast and heat.

In July, President Carter said he wanted to consult allies and make his decision on production of the new weapons "before the summer is over."

It was not until Tuesday, however, that the first consultation took place at NATO headquarters in Brussels. At that time a U.S. team, including Defense Department experts and scientists from the Energy Research and Development Administration, made a secret presentation before the NATO Nuclear Planning Group.

"We made no sales pitch," one participant said.

"They (the allies) were asked for their views without forcing them to take a position right then and there," said another official who was present.

When those replies will come seems in doubt. A State Department official said earlier this week, "There may be a continuing series of meetings until a consensus is conveyed to us." He added the process could take "until the end of the year."

A Defense official said a "timely response" was sought. "They're supposed to provide it some time next week," he said.

At the White House, a spokesman for the National Security Council said the allies' views are "expected in the near future" though the consultations could continue.

He added that the President's decision on neutron weapons production is not "firm . . . It could be weeks or longer."

When production funds for the weapons were discussed on the Senate floor, supporters pressed the idea they would be used on allied territory - a concept European governments found disturbing.

Left wing European parties and Communist organizations attacked the new weapons as inhuman, because they appeared to increase the prospect of slow death through radiation.

The debate grew particularly intense in Germany where it was discussed in the Bundestag.

Chancellor Helmut Schmidt and officials of his government shield away from announcing public support for the neutron weapons, saying instead that consultations are under way with the United States over their production.

Some officials in Schmidt's party have declared their opposition to the weapons while the more conservative German political parties have supported it.

In England, the ruling Labor Party has yet to make its position known and there are reports that some trade unions may raise opposition to neutron weapons at next month's Labor Party conference.

European concern may be ignited further when the House next week debates an amendment introduced by Rep. Theodore Weiss (D-N.Y.) and 11 other Democratic liberals to eliminate funding for the neutron weapons from the ERDA authorization bill. Appropriations for the weapons have already been approved by Congress.

When the money bill went through the House in June, little was known about the neutron weapons. Thus next week's debate will be the first time the matter has been discussed on the House floor.

Defending production of the neutron weapons will be at least two Democratic liberals, Rep. Thomas Downey (D-N.Y.) and Rep. Robert Carr (D-Mich.).

Downey, who has opposed many Pentagon weapons programs, calls the neutron weapons "defensive." He has suggested that the United States announce a policy of using the weapons only on allied territory if the Soviets agree to use their nuclear weapons only on Warsaw Pact territory.