Seoul — At the demilitarized zone, the South Korean officer, ramrod straight, was quietly pleased. ''To have President Reagan on the front line is a great honor for the Korean army,'' said Lt. Col. Kim Byong Kap. ''It will help build up espritm along this front. I feel like he's my senior family.''
President Reagan's trip to the Republic of Korea, including visits with US and Korean troops at the demilitarized zone (DMZ), has greatly reassured South Koreans in the wake of recent national disasters. Tensions had gripped this country following the shooting down of the Korean airliner and the bombing in Rangoon, Burma, of 17 South Koreans, including high Cabinet officials. Mr. Reagan's strong reaffirmation of the US commitment to South Korea's defense seems to have eased the anxiety.
Applause broke out in the National Assembly when the President declared: ''You are not alone, people of Korea. America is your friend and we are with you.''
Beyond the security reassurances to South Korea, Mr. Reagan achieved a number of foreign policy objectives during his six-day journey to northeast Asia. With a view to enhancing regional and global stability, he:
* Delivered a strong statement of American friendship for Japan, thus helping to alleviate Japanese unease about growing anti-Japan sentiment in the US Congress and within American industry. Some members of the Diet (parliament) were visibly moved when the President declared that the ''Japanese-American friendship is forever.''
* Laid the ground for progress in talks to resolve bilateral trade, finance, and defense problems. Japanese Prime Minister Yasuhiro Nakasone was spared the pressure of doing something before the Japanese elections in mid-December in hopes he can be more forthcoming next year.
* Heralded a ''new Pacific era'' in which the countries of northeast Asia and the Pacific would play an increasingly important role in global affairs, he thereby seemed to signal Europe that US foreign policy henceforth would be less Eurocentric.
* Gave a measured but unmistakable nudge to the South Koreans to develop democratic political institutions as an essential element of security.
* Kept open the door to a relaxation of tension on the Korean peninsula through a dialogue between North and South. ''Even as we stand with you to resist aggression from the north,'' Mr. Reagan told the South Koreans, ''we will work with you to strengthen the peace on this peninsula.''
How to reduce the hostility and tensions between the two Koreas has long been a dilemma of US policy, and the presidential trip served to highlight it. For the moment the issue of resolving the Korean division is dormant. Far from trying to find a way out of the dilemma, Mr. Reagan has mounted a campaign of diplomatic pressure to isolate North Korea after the Rangoon bombing. Japan is expected to announce new trade restrictions against North Korea and, according to US officials, Pakistan and others may follow Burma's lead in breaking off diplomatic relations with Pyongyang.
However, it is significant that before the bombing there were mounting signs of interest from many quarters in trying to defuse the East Asian ''powder keg.''
The North Koreans are reliably reported to have made overtures on the subject to China. The Chinese, in turn, brought up the issue of Korean peace when US Defense Secretary Caspar Weinberger visited Peking.
Before the events in Burma, Japan too had been trying to expand contacts with North Korea, including visits by Diet members, and the matter is expected to be raised when Chinese Communist Party Chairman Hu Yaobang visits Tokyo later this month.
South Korean leader Chun Doo Hwan also has put forward proposals to relieve tensions with the North, but the North Koreans are suspicious of all such moves because the effect would be the perpetual division of North and South. Rabid ideologues, they refuse to recognize the legitimacy of the South Korean government. All previous efforts to get a dialogue started, including proposals for a four-or-five power conference aimed at cross-recognition of the two Koreas , have foundered because of the North's refusal to talk directly with the South.
US officials say that, while the near-term prospects do not appear bright, especially since North Korea faces a succession problem, long-term prospects could be better because South Korea is such a going economic concern and the disparity between North and South is growing.
President Reagan took repeated note of the South Korean ''economic miracle.'' The fact that this is the first time a US president has come to Korea urging it to open its markets to American goods vividly bespeaks the enormous distance the Koreans have come economically.
South Korea's political process remains problematic, however. Some Koreans would have liked stronger support from Mr. Reagan in their effort to improve human rights in South Korea. While President Chun has taken some steps to increase political activity, he runs the country with an authoritarian hand.
''Chun's government has not yet strong support among the people themselves,'' said Rev. Park Hu Hyung Kyu, chairman of the human rights committee of the South Korean National Council of Churches, after a reception for community leaders at the US embassy. ''Popular support is still weak,'' Rev. Park said of Chun.
Rev. Park, apparently the only dissident present at the reception, was somewhat critical of Mr. Reagan, but said that the President's ''quiet diplomacy'' was doing ''something good'' for South Korea.
According to US officials, Mr. Reagan raised the issue of ''democratic rights'' with President Chun. He also mentioned the subject publicly more often than had any previous US president, including Jimmy Carter.
Throughout his Asian trip Mr. Reagan made frequent references to the barbarity and failures of communism. But he struck a moderate tone with respect to the Soviet Union, stressing his commitment to achievement of an arms control agreement. The President clearly sought to reassure the Japanese people that he is not a leader given to quick resort to military force, a stance which he hopes will help Prime Minister Nakasone politically as well as assure Americans back home.