Cheonan - a 1,200 tonne naval ship - sank minutes after an explosion on Friday just south of the disputed maritime border with North Korea.
Fifty-eight crew members, including the captain, were rescued, but 46 are still missing.
Though no direct evidence has yet emerged about North Korea's role in the sinking, the South Korean defence minister on Monday said mines floated by the North may have been behind the unexplained explosion.
"North Korea may have intentionally floated underwater mines to inflict damage on us," Kim Tae-young said.
North Korea made no mention of the sinking in its media but issued a warning on Monday about any military moves by the South and the United States.
"Any moves by the South could lead to unpredictable incidents," warned the statement issued by North Korea.
Slim survival chances
The rescue efforts have been hampered by murky water and strong currents at the site, combined with the high pressure of the water.
|President Lee Myung-bak, right, is overseeing the rescue operation [Reuters]
"Due to unfavourable weather conditions there has been no breakthrough in the current rescue operations," Lee Gi-Sik, the Navy's brigadier general, said.
Rescuers say sailors trapped in the sunken ship would have little chances of survival, having run out of oxygen.
"Divers pumped oxygen into the ship through cracks in the stern," Rear Admiral Lee Ki-sik of the joint chiefs of staff, said.
"The crew would have had only enough oxygen in their watertight cabins to last until Monday evening."
Lee Myung-bak, the South Korean president, on Tuesday ordered the military to be alert.
"Since the sinking took place at the front line, the military should thoroughly prepare for any move by North Korea," Lee said.