President Reagan yesterday began his last year in office by pressing for support for his arms control policies on both domestic and international fronts.

The president, who will leave office next Jan. 20, enlisted the help of former senator John G. Tower (R-Tex.) to help him guide through the Senate ratification process the recently signed treaty to eliminate U.S. and Soviet intermediate-range nuclear missiles. Arms control will be one of the major themes of the president's State of the Union speech Monday night.

The president raised the arms control issue yesterday with West German Foreign Minister Hans-Dietrich Genscher, who was visiting in his role as president of the European Economic Community, and an international group of labor leaders. Reagan also announced the dates for his trip to Europe to confer with NATO leaders.

Both the West German government and the labor leaders have endorsed the INF Treaty and Tower told reporters after a 15-minute meeting in the Oval Office that he believed it would be ratified by the Senate. The president's major concern is "to prevent any crippling amendments or reservations" that would force the United States to reopen negotiations with the Soviets, Tower said.

White House officials said that they want the treaty, which Reagan signed at last month's summit with Soviet leader Mikhail Gorbachev, to clear the Senate by a large margin, signaling to the Soviets that the administration worked to back its commitment to reduce nuclear arms.

Tower, who once chaired the Senate Armed Services Committee, led opposition to President Carter's SALT II treaty, which provided limits on long-range nuclear weapons. The treaty never was ratified by the Senate. Administration officials said Tower's role will be to ease the fears of conservatives that the United States cannot verify Soviet compliance with the INF Treaty.

Overwhelming ratification would help propel the Soviets to move quickly toward an agreement on strategic arms that Reagan hopes to sign at a summit this spring in Moscow, administration officials said. A large margin also would lessen the chances that Senate opponents would attach major reservations to the long-range arms treaty, the officials said.

Genscher was told that propects are good that agreement on the second treaty could be reached during the arms control talks underway in Geneva, White House spokesman Marlin Fitzwater said. "Both sides have a spirit of cooperation and intention to try to get an agreement by the May-June time frame," Fitzwater said.

Arms negotiations will be one of the major topics that Reagan and other NATO heads of state will discuss in Brussels March 2 and 3.

Fitzwater also announced that final laboratory results from the president's cancer checkup last week showed no recurrence of his prostate problem.