Sarah Jessica Parker Worries About Health of Surrogate Mom

updated 05/20/2009 AT 08:40 AM EDT

originally published 05/19/2009 AT 06:55 PM EDT

Sarah Jessica Parker says the surrogate mom carrying the actress's twins is a strong woman who made "an incredibly generous and gracious choice."

But Parker now worries that this strength is being put to too much of a test from the media attention following the announcement the Sex and the City star and husband Matthew Broderick are expecting twin girls.

"On a daily basis, on an hourly basis, I am greatly concerned for her health and safety and the safe delivery of our children," Parker, 44, tells Access Hollywood in an interview airing Tuesday.

Parker alleges that the surrogate, along with her friends and family, have been subjected to threats and harassment by the tabloid media. "Obviously there are those that don't care about her, or her health, or safety, or my children's health and safety, and that they should go to term and not go into an early labor and, God forbid, suffer all the things that can happen – that is a real possibly," she says.

Explored Variety of Methods

All this comes at what should be one of the happiest times in the lives of the couple, who turned to a surrogate out of necessity. "We have been trying to expand our family for a number of years and we actually have explored a variety of ways of doing so," Parker says. "It would have been odd to have made this choice if I was able to have had successful pregnancies since my son's birth."

The couple have also explained some of the surrogacy process with their 6-year-old son James Wilkie. "I've been pretty candid with him," she says. "I kind of chartered my own course with him because we wanted to keep this quiet and so I wanted to be very careful about telling him so he wasn't burdened with a secret. On the other hand, I wanted him to have time to adjust to the idea of sharing his mama and his papa."

The actress has high praise for the surrogate. "I'm really comfortable with her. She's made a really big choice to be part of our lives and I think she's an honorable person," says Parker. "You can't express enough how much you think about decisions like this ... She's strong, bright, independent, thoughtful, caring, gracious and generous."

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