"Our Anti-Trafficking and Anti-OSAEC (online sexual abuse and exploitation of children) task force in Cebu is currently investigating the matter," Nicholas Ty, Philippine justice undersecretary, told Reuters.
Reuters could not immediately reach Thomas Markle for comment but he was quoted by the Daily Mail newspaper in Britain as saying the allegations against him were untrue and "sick lies".
Meghan, who is American, married King Charles' younger son in 2018. In a statement, she said she was "deeply distressed" over the allegations, first published in Britain's Sun newspaper on Friday.
Meghan said in her statement that she had known about the allegations against her father, 82, since 2018 and had prevented him from having contact with her children Archie, 7, and Lilibet, 5, to protect them.
She has been out of contact with her father since the run-up to her 2018 wedding. Days before the event, Thomas Markle said he would not attend due to ill health after he earlier admitted posing for paparazzi pictures.
Philippine interior minister Jonvic Remulla told Reuters it was Markle's son, Meghan's half-brother, who is also called Thomas, who provided police with evidence of the allegations, including a laptop, confirming details in the Sun newspaper.
Meghan's father, who had lived in Cebu in the Philippines for some time, was now believed to be back in the United States, Remulla added.
Meghan said she was shown a letter which had been sent to British police in 2018 with "troubling and disturbing" allegations about her father, adding that she was told they were being investigated.
British police said they were aware of "media reports that officers from the Met's Royalty and Specialist Protection Command were involved in the passing on of a letter in 2018."
"We are undertaking inquiries internally in an effort to confirm this," a spokesperson for the Metropolitan Police said.
Meghan said she was "deeply distressed at the news that has come to light in the last 24 hours, and my thoughts are with any children who may have been harmed.
"My sincerest hope is that justice will be fully served and that the priority remains the safety and protection of innocent children," she said.
The Sun also said Thomas Markle's son had contacted the FBI in the United States over the allegations.
"The FBI is aware of the allegations and will provide support, as appropriate, to the Philippine authorities," the FBI said in a statement.
"We will also investigate any related allegations of federal violations of US law."
Harry and Meghan and their children relocated to England in August after living in California for six years.
1800 RESPECT (1800 737 732)
National Sexual Abuse and Redress Support Service 1800 211 028
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