By Chris Francescani

NEW YORK (Reuters) - French billionaire Francois-Henri Pinault was grilled on Friday -- the second day of a child-support trial in Manhattan -- about why he delayed accepting paternity of the child he had with supermodel Linda Evangelista.

Pinault, 49, who is currently married to actress Salma Hayek, has called Evangelista's demand of as much as $46,000 a month in child support unreasonable. Evangelista, 46, wants Pinault to provide for their son, Augustin, at a level on par with his daughter with Hayek.

During a heated exchange with Evangelista's lawyer, an exasperated Pinault said that Hayek had suffered through a traumatic pregnancy in which she almost lost their child, Valentina, who was born healthy in 2007 - a year after Augustin.

"What prevented me from...legally recognizing...was that my wife was pregnant, and it was a very difficult pregnancy," Pinault said.

"To be very clear - for five months we were told that the baby had Down syndrome. I asked Linda to delay recognition of Augie until the birth of Valentina," he said.

Pinault said Evangelista readily agreed. Hayek was not in court to hear her husband's testimony.

Later in the day, Evangelista - most famous for telling Vogue magazine in 1990 that models of her caliber "don't wake up for less than $10,000 a day" - testified for 45 minutes about her rise to the top of the modeling industry, saying that she can still command as much as $100,000 for a single publicity appearance.

Pinault is the chief executive of PPR - a multinational firm with a portfolio of companies that includes luxury brands Gucci and Yves Saint Laurent. Evangelista's lawyer contends that Pinault, who has two other children from a previous marriage, is worth more than $3 billion.

Pinault testified that Evangelista approached him with a child support request in 2007 that he found "unreasonable," but that she failed to respond to his counter-offer for three years, and then sued him for support in 2010.

Evangelista, whose delicate cheekbones and haunting gaze became an industry standard in the model-obsessed 1990s, wore an ivory white dress beneath a slate gray, collared linen jacket and beige stiletto heels on Friday.

During a break in testimony she declined reporters' inquiries about her wardrobe.

"I'm here today as a mother, not a model," Evangelista replied.

"But that's a question I normally like to answer," she added as she walked away.

Her testimony is expected to continue on Monday.

(Editing by Edith Honan and Lisa Shumaker)