The popularity of the ''Columbo'' detective series extends far beyond the borders of the United States.

When Emperor Hirohito visited the United States in the mid `70s, he was asked whether there were any famous Americans he wanted to meet. The Son of Heaven requested two American icons: John Wayne and Columbo.

The original series, which ran from 1971 to 1977, was so popular in Romania it was broadcast there twice a week. When ''Columbo'' stopped production in the U.S., suspicious Romanians thought their government had canceled the show because of import quotas. Fearing riots, the Romanian government begged the U.S. State Department to have the show`s star, Peter Falk, make a public-service announcement explaining the real reason for the demise of ''Columbo.'' Falk obliged and taped a TV spot, which he read phonetically in Romanian.

While Falk was shooting last summer`s film ''Vibes'' in the Andes mountains, 18,000 feet above sea level, children came running out of their huts when they saw him and screamed, ''Columbo! Columbo!''

''You think you`re in another civilization, another time, and then you see antennas coming out of these hovels, and your mouth falls open when you see the descendants of the Incas shouting `Columbo! Columbo!` '' says Falk in the studio adjoining his home where he spends hours doing charcoal sketches of women.

Reruns of ''Columbo'' in Japan regularly beat baseball broadcasts, a national mania. The series consistently tops ''Cosby'' in Paris. It`s also the No. 1 hit in Israel.

In the `70s, when Falk testified before Congress in his capacity as national chairman of Easter Seals, the government supplied him with bodyguards during his stay in Washington. As he was leaving the Capitol, two men dressed all in black rushed toward him. Falk`s bodyguards shoved him into the back seat of his limousine and fended off the attackers. It turned out the

''assailants'' were from Iran, bodyguards for an Iranian dignitary visiting the capital. They wanted Falk`s autograph.

The international popularity of ''Columbo'' doesn`t always translate into the red-carpet treatment abroad for the man who plays him.

Trying to leave East Berlin, Falk was detained by an obnoxious border guard enraged by an irregularity in Falk`s passport (the edges of the document were frayed, Falk says). The guard, who didn`t recognize the actor, ordered another guard to strip-search him. After the search, the second guard winked at Falk, then asked for an autograph.

PART OF PACKAGED TRIO

''Columbo'' returned this season as part of ''The ABC Monday Mystery Movie,'' broadcast every three weeks. The other two weeks are filled by ''B.L. Stryker,'' starring Burt Reynolds, and ''Gideon Oliver,'' starring Louis Gossett Jr.

In Chicago, the new ''Columbo'' is a huge hit. It beat ''Lonesome Dove''

in the ratings when it was shown opposite the miniseries, which was No. 1 in much of the country, and the last episode of the new ''Columbo'' ranked No. 8 in the local Nielsens.

Falk, 61, has his theories on the enduring popularity of the bumbling homicide detective with the decaying trenchcoat and `59 Peugeot.

''It`s his lack of pretension,'' Falk says. ''I think they like the fact that he looks dumb but he`s actually smart. They like the fact that he`s from the streets, and he`s been nailing people who should know better.''

William Link, who co-created the original ''Columbo'' and is co-executive producer of the new series, agrees with his old friend`s assessment. ''You get enjoyment out of seeing a very humble-appearing man who doesn`t appear to be too bright, but inside his mind you know there`s a computer that doesn`t miss anything. There`s a nice contrast there that appeals to you whether you`re an Arab or Japanese or in the Third World.''

Link thinks Falk is Columbo. ''He`s ingratiating, funny, droll, extremely bright,'' Link said. ''He loses things just like Columbo. Peter forgets his car keys, and they have to be messengered from his house. He has a big heart. When my partner (''Columbo'' co-creator Richard Levinson) died two years ago, Peter wrote me a very touching letter.''

Co-executive producer Richard Alan Simmons, who wrote the TV-movie, ''The Price of Tomatoes,'' which won Falk his first of four Emmys, disagrees with Link, his partner.

''Peter is not Columbo any more than the Little Tramp was Charlie Chaplin,'' Simmons said. ''Columbo is Peter`s creation. Don`t confuse him with Peter. He`s not like most TV actors who merely play reflections of themselves. He`s not simply extending his personality and calling it a performance.''

The truth seems to lie somewhere in between. Like Columbo, Falk fractures English and favors double negatives. Although his parents owned a successful clothing store in Westchester County, fashion is apparently not one of Falk`s preoccupations. The day I interviewed him he was wearing baggy polyester pants. His shirt was untucked and had come unbuttoned at the navel. When he finished a cigarette, he threw the butt on the floor.

FALK`S A POLI-SCI GRADUATE

Unlike Columbo, Falk is well-educated. He has a bachelor`s degree in political science from Syracuse University and a master`s degree in public adminstration from the prestigious New School of Social Research. As disarming as Columbo, he admits he plagiarized his bachelor`s thesis because of time constraints.

''I was in love and I wanted to go to Europe'' right after graduation, he says. He did write his master`s thesis all by himself, but he can`t remember what it was about.

His present surroundings are also part-Columbo and part Beverly Hills movie star. A late model Rolls-Royce and a Mercedes are parked next to his littered artist`s studio, which has unfinished walls and a cot whose sheets are unmade. The studio is attached to his home, a sprawling Palladian villa in a choice section of Beverly Hills.

Like Columbo, he can be very ingratiating. Falk recalled his appearance in ''Glengarry Glen Ross'' in Chicago three years ago.

''It was one of the best experiences of my life,'' he said. ''I love Chicago. It`s one of the great cities. I`m crazy about the town. It reminds me of New York when it was at its best, the New York that used to be and is no more. I love the architecture, the old stuff and the new stuff.''

Falk`s ingratiating personality made him the most popular kid in high school. He lettered in three sports at Ossining (N.Y.) High, despite the loss of an eye when he was 3 during surgery to remove a tumor. He was elected class president twice, ''and then I got barred. The principal wouldn`t allow me to run again. I got into some kind of trouble there.''