The 25-year-old Liverpool defender, who limped off during a friendly match against Costa Rica on Saturday, told Reuters his ankle was still swollen but he hoped to resume full training shortly.
"It's still swollen but it's getting better each day," he said, shouting over the sound of vuvuzela trumpet blasts from the local fans who watched Slovakia's first training session in the country at a small stadium in Pretoria.
"In the morning I'll be training with a personal coach and after that I hope to train with the team. We're a little bit tired after the travelling but we should be fine by tomorrow."
Skrtel, who is competing at his first World Cup, has become a key member of the Slovak team due to his aggressive tackling and quick pace, but his season has been hampered by injury after he broke a bone in his foot earlier this year.
On Wednesday he trained away from the rest of the squad and with a personal coach, working on upper and lower body strength and lunging on his ankle, but was also joking around and squirting water at nearby coaches.
Slovakia, competing at their first World Cup, face New Zealand on Tuesday, Paraguay on Sunday and Italy next Thursday.
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