The attack occurred Monday morning at Eagles Nest Park near Lescot Lane in Orlando.
The Florida Fish and Wildlife Conservation Commission said Glover was playing fetch with his dog when the gator attacked the pit bull and dragged it underwater.
"My (dog), he turned around, came to me, and he took off to run back again," said Eric Glover, referring to King, his 10-month-old pit bull. "And when he took off again, the gator came out, snatched him in front of the bank here and took him in. And that was it."
A trapper was called to the lake but did not capture the alligator. The trapper returned Tuesday afternoon and will remain until he catches the alligator, wildlife officials said.
FWC said an officer was in the area and "will maintain vigilance in and around the area to support the trappers' efforts."
Several houses back up to the lake, which is near Kirkman Road and Raleigh Street. A bike path and jogging trail outline the edge of the lake. Neighbors said many children take the path every day to and from Eagle's Nest Elementary School.
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