The Reagan administration called on North Korea yesterday to cooperate in "lessening conflict and strengthening regional peace" around the divided peninsula and promised the United States "will do our part" in encouraging change.

In the first U.S. policy speech on the subject since South Korea's recent acceptance of direct presidential balloting after weeks of protests, Assistant Secretary of State Gaston J. Sigur also pledged U.S. neutrality and said, "We lend our full support -- unqualified -- to the Korean people and whichever candidate they choose to be their next president in an open and fair election."

Sigur, who visited Seoul last month as the South Korean government and ruling party were moving to accept opposition demands for a direct election, said yesterday, "We lend our full and enthusiastic support to the process, but not to any individual or party."

Most of his address to the Foreign Policy Association in New York was devoted to North Korea because the administration has said so much recently about political developments in South Korea, according to State Department officials. While announcing no new policy initiatives, the speech was notable for its relatively restrained tone toward the communist North and its emphasis on possible future improvements within North Korea, in North-South relations and in the U.S. role.

Washington also informed North Korea in March that it was prepared to take major steps, such as easing the near-total ban on trade with the United States, if North Korea would participate in next year's Summer Olympic games and resume North-South talks. State Department officials said the offer remains, though North Korea has not yet met either condition.

North Korean representatives did not accept the latest and "final" offer of the International Olympics Committee (IOC) at Lausanne, Switzerland, last Wednesday to participate in the 1988 Olympics as host for several events.