The family of the American missionary kidnapped in Nigeria have said she is "doing God's work", with friends praising her "relentless" courage.

Rev Phyllis Sortor, a missionary with the Free Methodist Church, was abducted from the Hope Academy compound in Emiworo, Kogi state, on Monday morning.

Mike Henry, staff pastor of the Wenatchee Free Methodist Church in Washington state, has worked with Sortor on charity projects in Nigeria the past. He told AP that the missionary, who grew up in Mozambique, was his "inspiration of courage".

A spokeswoman for Seattle Pacific University, which Sortor attended in the 1960s, said the college was "proud of her untiring service to God and the people of Nigeria".

"[We] are earnestly praying for her safety and immediate release," she added.

"She believes in God, she's doing God's work," Sortor's stepson, Richard, told reporters at a prayer service on Monday night.

The news of her abduction is "surreal, just surreal, I can't believe this," he added.

The Kogi Police Commissioner, Adeyemi Ogunjemilusi, told NBC that five armed men jumped over the walls of the compound at around 10.30am local time, firing shots into the air. Sortor was likely the target of the raid because no one else was taken, Ogunjemilusi said, and her abductors have demanded almost $300,000 for her return.

Kidnapping is a major criminal enterprise in Nigeria, making millions of dollars every year. Sortor is one of many expatriates to have been abducted in southern and central Nigeria, and Ogunjemilusi said it was unlikely to be the work of militant group Boko Haram, which does not usually operate in the area.

Brenda Young, lead pastor of Cornerstone Free Methodist Church in Akron, Ohio, described Sortor as "relentless. She's very courageous. She perseveres."

Young worked with Sortor on a clean water project in Nigeria. "She's one of the most devoted, compassionate, hard-driving women I've ever known," she said of her colleague.

"Her feeling was that these were her people, and that she loved them. She felt like this is where she was supposed to be."

A video has emerged online from 2009, in which Sortor thanked friends for paying her late husband's hospital bills.

"I know that nothing that can happen to me in my future can ever defeat me with God by my side," she said.