Burnham, 43, was rescued Friday when Philippine soldiers ambushed her kidnappers, members of the Muslim extremist Abu Sayyaf group. Her husband, Martin, and Filipino hostage Ediborah Yap were killed in the two-hour shootout.
Burnham was greeted with hugs by her children Jeff, 15, Mindy, 12, and Zach, 11. The children had been living at the Rose Hill home of Martin's parents, Paul and Oreta Burnham.
Gracia Burnham talked to reporters briefly and said she supports government efforts to assist the Philippines in ridding the country of terrorists.
"A very bad thing happened to Martin and I when we were taken," she said. "Please know that God was good to us very single day of our captivity. Martin was a source of strength to all the hostages. He was a good man and he died well.
"It's good to be home. Keep praying for me and my kids as we begin to rebuild our lives, and thank you."
Before leaving the Philippines Sunday, Burnham also spoke with reporters from a wheelchair, her right leg bandaged after a bullet tore through it during the gun battle that freed her.
"I return to the States this morning to rejoin my children and to put my life back together. Part of my heart will always stay with the Filipino people," she said, reading from a statement.
Her voice broke with emotion and tears glistened in her eyes as she mentioned her husband, Martin, who was killed, along with Filipina nurse Deborah Yap, in the shoot-out between government troops and Abu Sayyaf Muslim rebels in the southern Philippines.
The body of Martin Burnham, who was 42, has been flown to a U.S. military base in Japan is expected to be flown to the U.S. later this week.
President Gloria Macapagal Arroyo said Saturday the Philippine air force and army will now unleash their full arsenal the rebels have no more hostages.
The Burnhams, from Wichita, Kansas, were abducted from a tourist resort in May last year and held for a year and 11 days in the Philippines' longest hostage saga involving foreigners.
Married for 19 years, they had been working as missionaries in the mainly Catholic country for 15 years for the Florida-based New Tribes Mission (NTM).
Burnham, wearing a bright red shirt, called her captors criminals who deserved to be brought to justice.
"During our ordeal, we were repeatedly lied to by the Abu Sayyaf and they are not men of honour. They should be treated as common criminals. We support all efforts of the government in bringing these men to justice," she said.
Gracia avoided references to how her husband died.
Fragmentary accounts from her family indicated she might have been saved when Martin fell over her after he was shot, shielding her from further gunfire.
"She thought she lay there for about 20 minutes," Gracia's younger sister, Mary Jones, said in an interview on Manila television.
"She said that after that 20 minutes, he just became very heavy. She said that it was very peaceful and she was glad that she was able to be with him when it happened."
U.S. embassy spokesman in Manila Frank Jenista said Gracia Burnham reported 17 gunbattles between government troops and Muslim rebels during their captivity.
Burnham beamed when she entered an airport lounge where a crowd of reporters had waited for hours for her first public appearance since her dramatic rescue.
But the cheerful facade cracked when she pulled out a pad of paper and read her statement. Her heavily bandaged leg was stretched out in front of her on a top of a pillow.
But her emotion masked an inner strength, said Scott Ross, a spokesman for the Florida-based organization that sponsored the Burnhams and other missionaries around the world.
"She is upbeat, she really believes that God is in control, and that for whatever reason, it was meant to be," said Ross.