Shaima Alawadi, 32, was taken off life support on Saturday, three days after her 17-year-old daughter found her unconscious in the dining room of the family's El Cajon home in suburban San Diego.
Investigators said they're exploring all aspects of her slaying, including the possibility that the attack was a hate crime.
Alawadi's father is a Shiite cleric in Iraq and the Iraqi government will pay for have her body sent back, a Muslim leader in Michigan told the Detroit Free-Press on Sunday.
"Everybody is outraged," Imam Husham Al-Husainy of the Karbalaa Islamic Education Center in Dearborn said. "This is too evil, too criminal."
The daughter, Fatima Al Himidi, told KUSI-TV her mother had been beaten on the head repeatedly with a tire iron, and that the note said "go back to your country, you terrorist."
Police said the family had found a similar, threatening note earlier this month but did not report it to authorities.
Al Himidi told KGTV-TV her mother dismissed the first note, found outside the home, as a child's prank.
Flowers were piled on the doorstep of the home Sunday. A neighbor said the family had moved in only a few weeks ago.
Friends said Alawadi wore a hijab, the Islamic head scarf.
Hayder Al-Zayadi, a family friend, told the Free-Press Alawadi moved to the United States in 1993 with her family and was part of a wave of Shiite Muslim refugees who fled to Michigan after Saddam Hussein cracked down on an uprising in 1991.
After living in Dearborn for a few years, she moved to the San Diego area in 1996, graduated from high school and became a housewife raising five children, Al-Zayadi said.
Al-Zayadi said Alawadi's brothers worked for the U.S. Army, serving as cultural advisers to train soldiers who were going to be deployed to the Middle East. Another family friend told the San Diego Union-Tribune that Alawadi's husband had a similar job.
El Cajon, northeast of downtown San Diego, is home to one of the largest Iraqi communities in the United States.