President Reagan taped a New Year's message to the Soviet people yesterday to be shown on television there on the holiday, a White House spokesman said.

Marlin Fitzwater said Soviet leader Mikhail Gorbachev is taping a reciprocal message for the holiday and U.S. television networks are being asked to air it. Fitzwater said it is up to the networks and "if they don't want to do it, they don't have to."

He said the networks declined to give any commitment but he thought they would broadcast the Gorbachev speech.

If there is no agreement on joint airing of the three- to five-minute tapes by the superpower leaders, written messages will be exchanged.

Fitzwater said if the Gorbachev message is broadcast, it is expected to air at noon on New Year's Day in the United States and the Reagan message at 9 p.m. EST in the Soviet Union on the holiday.

The Soviets celebrate the New Year's holiday with traditional family doings and sending cards.

Messages of good will have been exchanged from time to time between Soviet and U.S. leaders on the holiday.

This holiday's exchange comes with relations between the two superpowers on the upswing after the Washington summit meeting this month, at which Reagan and Gorbachev signed the Intermediate-Range Nuclear Forces (INF) Treaty.