Lamas, who was 16 weeks pregnant, was rushed to the hospital Sunday night after she collapsed at her home, TMZ reported Monday. Doctors determined she was bleeding internally and performed emergency surgery during which her baby died, the website said.
Lamas was later placed in a medically induced coma and was breathing on a ventilator.
"We would like to thank everyone from the bottom of our hearts for the immense support we have received from our family, friends, fans, and media," Richie said in a statement to UsMagazine.com Tuesday.
"It is really amazing how everyone has come together for Shayne, Press, and I during this extremely difficult time," the statement said.
"Shayne is breathing on her own now and doing better; we have high hopes for a speedy recovery. At this time we are still trying to process everything that happened and we thank everyone again for giving us this time to heal."
Lamas married Richie in 2010. Their daughter Press was born in November 2011.
Lamas, 28, is the daughter of actor Lorenzo Lamas. She is known for her work on TV's "General Hospital" and in the reality TV shows "The Bachelor" and "Leave it to Lamas."
"We are so very grateful to the hospital personnel and the doctors who saved her life last night," Lorenzo Lamas said in a statement Monday. "Shayne is aware of her condition and that her family and her husband are here with her and love her so much. She will be remaining in the hospital until her doctors determine that she can be released."