The satellite, designed to monitor climate change, had been due to separate from the rocket at an altitude of 302km and to deploy its solar panels about nine minutes after blast-off.
The rocket had only reached an altitude of 70km when the apparent explosion occurred.
"I cannot definitely say now, but there appears to have been a problem with the first stage of the rocket," Lee Jae-Woo, a space expert at Konkuk University in Seoul, the South Korean capital, said.
The first stage of the liquid-fuelled rocket was made in Russia, while the second stage of the rocket and the satellite were built domestically.
The remnants of the rocket might have crashed into the ocean about 465km from Seoul, officials said.
This is the second time a South Korean built rocket has failed in the past year.
A previous launch attempt failed in August when the nose cone of the satellite did not open properly.
South Korea has invested more than $400m in the 140 tonne Naro-1 rocket, with space technology seen as a matter of national pride for many Koreans.
About 100 people cheered as they watched the rocket's launch on television screens in the main railway station in the capital.
The mood at the station turned anxious when news of problems with the launch became apparent.
"We are sorry for failing to live up to people's expectations," Ahn said.
The country has previously sent 10 satellites into space, but has relied on launch vehicles and technology from other countries.
South Korea is aiming to catch up with Japan, China and India who are Asia's current space powers.
Japan has launched numerous satellites, while China sent its first astronaut into space in 2003 and carried out its first spacewalk in 2008.
India launched a satellite into moon orbit in 2008 but had to abandon it nearly a year later after communication links snapped.
The first South Korean astronaut was sent into space aboard a Russian Soyuz rocket in April 2008.
Lee Myung-bak, South Korea's president, has urged the country's space engineers and experts to avoid feeling frustrated over the failure and to aim for success in the future.
"Though it is regrettable, much more can be learned though failure," Lee said in a statement posted on the presidential website.
Ahn has said plans are underway for a third attempt to send a satellite into orbit, although he did not specify a date.