Two children from the United States have been rescued, cold but not seriously hurt, after spending the night alone in a forested area of Burke Mountain in Coquitlam, B.C.

RCMP say the six-year-old girl, seven-year-old boy and their father fell down a "steep, treacherous cliff" into a creek drainage area near Munro Lake late Sunday. They'd been trying to get to the lake to do some fishing on the sunny afternoon, but lost the trail, search crews said.

A police statement said the father made the difficult climb back up the hill, while injured, to get help. Search and rescue teams found the children just before 8:30 a.m. PT on Monday. They were rescued by long line an hour later, with their father standing by.

"This was really a miraculous rescue and a really positive outcome," Coquitlam Search and Rescue manager Ian MacDonald told reporters.

"You can imagine, all of us [searchers], we've got kids. It was really elation. This is very rugged terrain where they were lost so we were just very, very thankful that they were found alive and uninjured," he said.

Longline rescue of 2 children lost after Burke Mnt fall over cliff. Headed to safety at Minnekhada Park after long night without dad <a href="https://t.co/PysDS2WsVK">pic.twitter.com/PysDS2WsVK</a> —@ybrend

MacDonald said the children were cold but alert without any serious injuries. They were taken to Royal Columbian Hospital in New Westminster, B.C., for a full checkup.

Bryan Moffatt and Brad Rennie, who both work with Ridge Meadows Search and Rescue, were part of the team that found the kids.

"They were invisible, pretty much like a rock. They were hiding under a grey sweatshirt. After several calls, they actually responded and came out of the sweatshirt and gave us the A-OK," said Rennie, whose group spotted the children from up the hill.

Bryan Moffatt and Brad Rennie, both with Ridge Meadows Search and Rescue, helped look for the two children overnight on Sunday. They were part of the team that found the kids on Monday. (Tristan LeRudulier/CBC)

Asked if the kids were happy to see them, Moffatt laughed.

"Very," said Moffatt, whose own two kids are of a similar age. "They were quite smiley."

Kids 'did a great job'

Coquitlam RCMP Staff Sgt. Paul Vadik said the children were conscious when their father made the "difficult decision" to leave them Sunday night, thinking the climb would be too dangerous for the kids.

He wrapped them in warm clothes, told them not to move and hiked a kilometre or two over dense, forested terrain until he had cellphone reception to call for help. MacDonald said search crews got the call around 7 p.m. and searched for the children all night.

MacDonald said the children didn't move while they waited for rescue. They were found just where they'd been left, not far from a backpack their father had lost.

Search and rescue team members in the area where the children were found shortly after the rescue. (Ridge Meadows Search and Rescue)

"The kids did a great job. And the dad did a great job of telling them, you know, 'I want you to stay here,'" the search manager said.

"I suspect his reaction [to the rescue] is pretty emotional," MacDonald added.

He said the area around Munro Lake is safe so long as hikers stay on the trail, though it's common for people to get lost. Crews said the family was visiting from the state of Georgia and the father wasn't familiar with the area.