Birkhead, accompanied by his relatives, visited Dannielynn several hours after Tuesday's announcement of the DNA test results, "Entertainment Tonight" reported. The former boyfriend changed his daughter's diaper and fed her apple sauce with some coaching from Smith's lawyer-turned-partner Howard K. Stern, the program reported.
A hearing is scheduled for Friday during which a judge is expected to discuss who will raise 7-month-old Dannielynn. Stern, who has been caring for the baby since Smith's sudden death in February, said he wouldn't fight for custody, but a lawyer for Smith's mother, Virgie Arthur, indicated she might.
Birkhead said Wednesday he did not want another legal fight.
"We might go from one fight to another, but I'm hoping that's not the case because, you know, there's only one dad, and I have no problem with anyone that has good intentions being allowed to visit the baby and see the baby and be a part of the baby's life," he told NBC's "Today" show from the Bahamas.
Birkhead said, however, he has no intentions of sharing custody of the child.
"It would imply that I'm unfit as a parent, which I'm not," the Los Angeles photographer said. "I'm looking forward to giving Dannielynn everything that she needs and all the love and support."
Stern said Tuesday he loved the baby despite the DNA results and would support Birkhead.
"I'm obviously very disappointed, but my feelings for Dannielynn have not changed," he said, adding of Birkhead: "I'm going to do whatever I can to make sure he gets sole custody."
Birkhead said he believes Stern gave up his custody fight because he wants what is best for Dannielynn. He said the "dirty laundry" being aired in the courtroom is "something the baby could see one day."
Separately, a hearing was scheduled for Wednesday in the Bahamian Coroner's Court to check the status of an appeal filed by Stern that stalled the inquest into the death of Smith's 20-year-old son, Daniel.
Birkhead, who broke up with Smith before she moved to the Bahamas in July, had been seeking custody of Dannielynn for months. Stern was listed on the birth certificate as the baby's father and has been taking care of the child at the oceanfront mansion he and Smith shared in the Bahamas.
Dannielynn Hope Marshall Stern stands to inherit a fortune if the legal battles her mother left her ever get resolved.
The baby could potentially inherit millions from the estate of Smith's late husband, J. Howard Marshall II. The former model had been fighting the Texas oil tycoon's family over his estimated $500 million fortune since his death in 1995, and that battle remains unresolved.
It remains unclear how much, if any, of the Marshall estate Dannielynn could ever hope to obtain, and whether her guardian would have any access to the money.
Even Smith's own estate remains unresolved. A 2001 will released after her death in February said her fortune should be held in trust for her son, but he's dead now. The 19-page will named Stern as her executor, but did not say how much Smith was worth or how much her daughter might inherit.
Nassau has been transfixed by the Anna Nicole saga since she moved here last year. Smith gave birth to Dannielynn in September, only to see Daniel die days later at her bedside from a lethal combination of drugs. Smith died on Feb. 8, at the age of 39, also from a deadly mix of prescription drugs.
Smith's mother said Tuesday that she wanted to be present in her granddaughter's life, but seemed appeased by the DNA results.
"I'm happy that Dannielynn will know who her real father is," she said.
Although fatherhood will be a new role for Birkhead, he has said it is one he is prepared for.
"She's got lots of toys and a nursery ready for her and she's got everything she's going to need. All I have do is just give her the love," he told the "Today" show.
Birkhead has said he met Smith, a former Playboy Playmate, at a Kentucky Derby party in 2003 but that they didn't start dating until he saw her at the same event the following year.
She had lost weight, was much friendlier than she had been the year before and invited him to accompany her to other events to take photos "and one thing led to another," he told Fox's Greta Van Susteren in January.
"We had, you know, even though it sounds like we battled and battled, but we had a great time in our relationship," he told Van Susteren.
Birkhead has said that he and Smith remained together until May 2006 when she was five months pregnant with Dannielynn.