2 American women were lost at sea for months. Then came Navy - and 'pure relief.'

The moment the two women and their dogs were finally rescued is captured on video, taken from the deck of a Navy boat.

The camera wobbles as the motorboat cuts across the ocean, some 900 miles southeast of Japan, toward the lone sailboat that had been sending distress signals for months after its engine died.

One of the women is on the deck, her arms outstretched.

She feverishly blows kisses toward the rescue boat. This is the reaction of someone who had been lost at sea for months.

"They saved our lives," rescued sailor Jennifer Appel said, according to a Navy news release. "The pride and smiles we had when we saw [U.S. Navy] on the horizon was pure relief."

"When I saw the gray boat on the edge of the horizon, my heart leapt," Appel said on NBC's "Today" show. "Because I knew we were about to be saved. Because I honestly believed we were going to die within the next 24 hours."

Appel and Tasha Fuiaba, both from Honolulu, had set sail for the Polynesian island of Tahiti in the spring.

But their boat's engine died in May after a bout of inclement weather.

They pressed on, hoping to make it to land by sail, the Navy said. But they soon found themselves lost.

Fuiaba told the "Today" show that she kept watch at night, sending distress calls and flares when other vessels were within sight. "And when they would turn or keep going," she said. "Yeah, it was kind of sad."

Their distress signals, in fact, went unanswered for months. The Navy said that "they were not close enough to other vessels or shore stations to receive them."

The pair had prepared for a long trip; they had water purifiers and over a year's worth of food on board, mostly dry goods including oatmeal, pasta and rice.

But, at times, there were still other dangers surrounding them: sharks.

Appel told the "Today" show that she once took the dogs downstairs and "we basically laid huddled on the floor and I told them not to bark because the sharks could hear us breathing. They could smell us."

Appel said in a conference call with reporters from the Ashland that the pair sent a distress signal for 98 days.

"It was very depressing and very hopeless, but it's the only thing you can do, so you do what you can do," she told reporters, according to the Associated Press.

When asked whether she thought they might die, Appel responded that it was only human to believe that.

"There is a true humility to wondering if today is your last day, if tonight is your last night," she told reporters.

On Tuesday, a Taiwanese fishing vessel came across their sailboat, "well off its original course."

The fishermen alerted the U.S. Coast Guard, and on Wednesday, the USS Ashland, a warship operating out of Sasebo, Japan, tracked them down and dispatched the rescue boat.

The two sailors and their two dogs were brought safely aboard after the Navy determined that their boat was no longer seaworthy.

Once aboard the Ashland, they were assessed by medical staff and given food and lodging arrangements. The Navy said that they will remain on the ship until its next port of call.

Photos distributed by the Navy show the women smiling aboard the warship. Zeus the dog appears in good spirits, if a bit skinny.