SEOUL (Reuters) - South Korea said on Monday it was on guard for the possibility North Korea may try to snatch its citizens abroad or conduct "terrorist acts" after the North accused it of abducting North Korean workers from a restaurant in China.

"All measures of precaution" were in place for the safety of South Koreans abroad including an order to beef up security at diplomatic missions, said the South's Unification Ministry, which handles issues related to the North.

"We are on alert for the possibility that the North may try to abduct our citizens or conduct terrorist acts abroad," ministry spokesman Jeong Joon-hee told a briefing.

The two Korea's have been fierce rivals since the 1950-53 Korean War and tension on the peninsula has been high since January when North Korea conducted its fourth nuclear test. It followed that with a string of missile tests in defiance of U.N. Security Council resolutions.

South Korea said in April 13 North Korean workers at a restaurant run by the North in China had defected. North Korea accused the South of a "hideous abduction".

North Korea proposed sending family members of the 13 to South Korea for face-to-face meetings but the South rejected the suggestion.

About 29,000 people have left North Korea and arrived in the South since the Korean war, including 1,276 last year, with numbers declining since a 2009 peak. In the first quarter of this year, 342 North Koreans arrived in the South.

(Reporting by Jack Kim; Editing by Robert Birsel)