The father of tennis great Serena Williams said he thought his daughter was going to die when she was rushed to a Los Angeles hospital in March with a blood clot in her lung.

Richard Williams told reporters he feared the worst and is still amazed she survived.

"I thought she was going to die," he said. "I don't even know how she lived through it."

But Serena said she was strangely relaxed during her health crisis. "I actually was really calm. I didn't want to alert my parents or my family or anything," she told a news conference after beating Victoria Azarenka 6-1, 7-6 (5) at the US Open on Saturday.

"I think that's the calmest I've ever been in my life."

Doctors discovered the blood clot after she had travelled to New York for treatment on a foot injury that had sidelined her for months.

The 29-year-old badly cut her foot on broken glass at a restaurant in Germany after she won last year's Wimbledon title and underwent two operations because of complications with the injury.

The Williams family had to deal with another health scare at the US Open when Serena's older sister Venus pulled out, due to an autoimmune disorder. "She's doing better," Serena said. "You know, it's a day at a time kind of thing. Her spirits are better."