President Carter spent last night with American troops stationed in South Korea and then began a delicate diplomatic mission of showing support for the country's security without appearing to embrace a government that persistently is at odds with his human rights policy.

Carter rode in a motorcade through crowd-lined streets after being welcomed by President Park Chung Hee and then sat down with Park for two-hour discussion of human rights and Carter's controversial plan - now suspended - to withdraw American combat troops from South Korea.

Sources said Carter would not reveal his decision on the troop with drawal while he is here.

Carter spent the night with American soldiers at Camp Casey, headquarters of the Second Infantry division, which he has promised to withdraw eventually. The camp is about 12 miles south of the Demilitarized Zone that separates North and South Korea.

Then he drove to Seoul for a formal welcoming ceremony with Park. They shook hands, reviewed some troops, greeted dignitaries and then drove to the Blue House, Park's official residence.

The streets were lined with South Koreans waving flags and cheering, one of Carter's largest crowds overseas. The government, which had announced a plan to turn out a half million people, had urged government workers and students to attend the display of support for Carter.

After arriving last night from the Tokyo summit, Carter arose before 5 a.m. and went jogging with Second Division Brig. Gen. Robert C. Kingston and about 120 American troops. The troops chanted:

"Raise your eyes and what do you see - Mr. President is running with me."

In a breif speech to a signal corps unit at Camp Casey early today, Carter reminded troops that more than 50,000 American soldiers died in the Korean war 30 years ago.

They "gave their lives for principles in which we still believe," Carter said, including "the principle that people should be permitted to live in peace, free of the threat of successful aggression and the right to live in freedom."

Carter's schedule seemed to underscore a desire to keep a certain distance from Park, whose proclamation banning public dissent is a conspicuous breach of the human rights policy Carter announced shortly after taking office.

The South Korean government however, was dramatizing a closeness between the two leaders. Huge pictures of them dominate several city streets. Government-guided newspapers this week minimized past differences, published almost nothing about disagreements over civil liberties and predicted a joint communique stressing friendship between the two countries.

Carter had promised before leaving Washington to hear the views of South Korean opposition leaders but the schedule makers had left little time. He is scheduled for only five minutes in private with the opposition party's new chairman, Kim Young Sam, a strong critic of Park.

Carter's meeting with religious dissidents, according to a government spokesman, wil merely be part of a meeting with about a dozen religious leaders who represent "a diverse specrum" of opinion.

In two demonstrations recently and in a number of public statements, disident leaders have protested that Carter's visit amounts to a stamp of approval of Park's government and some asked him not to come.

According to the Korean National Council of Churches, at least 63 prominent critics have been under house arrest during the last 10 days and several of them contend that Carter's visit prompted the restrictions.

The government issued a statement saying that it is "deeply regrettable" that a "small number of people" are engaged in opposition to the Carter visit, "often defying laws of the nation."

How Carter treats the subject has become a central issue of the president's visit. Dissidents are looking for a strong statement deploring repression and clearly directed at the Park government.

It was understood that religious leaders would ask him to support three steps: an end to the presidential proclamation that bans public criticism of the government, the release of an estimated 340 persons arrested for violating it and a positive guarantee of free speech.

Carter said in 1977 all of the ground troops would be pulled out in four or five years. Last year he delayed withdrawal of the first contingent and has suspended further withdrawals pending a reassessment. One combat battalion and support forces, numbering about 3,500 troops, were sent home in December and about 31,000 remain.

Park was expected to press his cases for leaving troops here and his position has been strengthened by recent U.S. intelligence assessments that estimate North Korean strength in troops, tanks and artillery to be considerably greater than once believed. The U.S. Joint Chiefs of Staff have opposed resuming the withdrawal. CAPTION: Picture 1, President Carter enjoys his morning jog in South Korea before meetings with officials there. AP; Picture 2, South Korean President Park Chung Hee escorts President Carter to an awaiting helicopter. AP