The Senate voted 47 to 42 last night to loosen the strings that Congress attached last month to construction of facilities for production of a new nuclear artillery shell that can be made into a neutron weapon.

It also reiterated its 1982 call for a summit conference between President Reagan and Soviet President Yuri V. Andropov as soon as possible to work for "mutual, equitable and verifiable reductions in nuclear arms." The vote on the non-binding resolution, proposed by Sen. Arlen Specter (R-Pa.), was 82 to 7.

The actions came as the Senate ambled through a second day of work on its $200 billion defense authorization bill for next year, prompting Senate leaders to chastise colleagues for dawdling and warn of evening and weekend sessions unless the pace quickens.

The nuclear weapon reversal was proposed by Armed Services Committee Chairman John G. Tower (R-Tex.) and approved over objections from several Democrats who contended that the weapon was both unneeded and unwanted by NATO countries on whose soil it is to be deployed.

In action on an energy-water appropriations bill last month, Congress approved preliminary production funds for the new weapon but stipulated that none can be spent until a NATO country agrees publicly to accept the weapon. The bill is awaiting signature by President Reagan.

Tower's proposal would drop the NATO condition and let the money be spent if the president finds it to be in the interests of national security. He said the United States should not let its defense policy be dictated by foreign governments.

Arguing against Tower's proposal, Sen. J. Bennett Johnston (D-La.) contended that no NATO country will accept the weapon. European governments have recently opposed deployment of neutron weapons, which kill mainly by radiation rather than heat and blast, on several grounds, including a contention that it would make nuclear weapons easier to use.

"It is the lowest priority nuclear weapon," Johnston said.

In earlier action, the Senate cleared a hurdle that Democrats had posed on Monday to call attention to administration-inspired cost reestimates that enabled the Armed Services Committee to keep multiyear funding for the B1 bomber and still stay within budget targets.

But several senators, including Sen. Slade Gorton (R-Wash.), were considering a move to send the bill back to committee to restore the original figures.

In action on non-controversial amendments, the Senate also approved a proposal by Sen. Robert J. Dole (R-Kan.) to require the secretary of defense to report to Congress when the Pentagon plans to go ahead with production of weapons that have not undergone successful operational testing.

The secretary would have to explain why the weapons systems did not pass their tests and assess the risks and benefits of proceeding with production.