"My wife, Michelle, will be relieved," he told the military personnel gathered in a hangar at a Royal Australian Air Force base in the Northern Territory capital, Darwin.
"I have to admit that when we reformed health care in America, crocodile insurance is one thing we left out," Obama added.
A framed policy certificate was handed to the president by Northern Territory chief minister Paul Henderson. The $10 policies are issued by a local insurance company, TIO, which agrees to pay out $50,000 Australian dollars ($51,000) in the event the policy holder is killed by a crocodile.
"It's a unique product for a unique environment and we're excited to be issuing one of these policies for Obama as a memento of his time in the Territory," said TIO chief executive Richard Harding.
Obama is the first U.S. president to travel to Darwin, a remote city some 2,000 miles northwest of the Australian capital, which was bombed by the Japanese during World War II. A U.S. Navy destroyer, USS Peary, was one of eight ships destroyed during the Feb. 1942 bombing, and Obama visited a memorial in honor of the 89 men who perished on the vessel.
Obama's brief visit to Darwin with Australian Prime Minister Julia Gillard was designed to thank Australian troops, including those who have served or are serving in Afghanistan and Iraq.
Earlier in the day, addressing the Australian Parliament in Canberra, Obama noted the long history of Americans and Australians fighting side by side.
"From the trenches of the First World War to the mountains of Afghanistan, Aussies and Americans have stood together, we have fought together, we have given lives together in every single major conflict of the past 100 years," he said. "Every single one."
According to an agreement announced by Obama and Gillard on Wednesday, from mid-2012 the Northern Territory will host 250 U.S. Marines for six-month rotations, for training and as a base for humanitarian and military operations in the region. The number will gradually build up to 2,500 by 2016.