(CNN) -- The Coast Guard says it has done all it could to find teen boaters Perry Cohen and Austin Stephanos.
But their families say a private hunt for the 14-year-olds will press on.
The Coast Guard's weeklong search for the two Florida teens, who went missing at sea during a burst of severe weather on July 24, will stop at sunset Friday, after an extensive coastal search that extended from southern Florida to North Carolina, Capt. Mark Fedor told reporters in Miami.
Searchers found the teens' boat Sunday, dozens of miles off Florida's Atlantic coast, well north of Jupiter, the community the pair left days earlier.
"We believe we reached the limit for our effective search and rescue efforts," Fedor said.
The Coast Guard had estimated that someone could survive in the warm Atlantic waters for up to five days this time of year, and that the search went until Friday in part because the boys could have been in the boat until Sunday, when it was found capsized.
The teens' families, however, say a private search for Perry and Austin will continue, drawing on a GoFundMe campaign that has raised more than $299,000 to pay to fly private aircraft and buy boat fuel.
"Our families are committed to continue the search and rescue efforts of our boys with the aid of volunteer pilots and aircraft," the families said in a joint statement.
"We would like to express our heartfelt gratitude to our families, friends, neighbors, colleagues, community, along with strangers from around the globe for your prayers and thoughts as well as all that have contributed to the Perry and Austin Rescue Fund to ensure the boys' safe return," the statement reads.
Missing after a squall
Austin and Perry left Jupiter in a 19-foot, single-engine vessel on July 24. The Coast Guard said it had information that the boys may have told others through social media that they planned to travel to the Bahamas, but officials and family members say they're not sure the purpose of the boys' trip and the destination.
Fedor said a significant squall hit the area about the time they left -- one that that could have disabled or even capsized their boat. The National Weather Service posted special marine warnings, telling boaters to seek shelter about the time they departed.
Later that day, when one of the boys' grandmothers didn't hear from them, she reported them missing.
The teens' boat was found Sunday, 67 nautical miles (about 77 miles, or 124 kilometers) off Florida's Ponce de Leon Inlet.
One life jacket was found in the water, but there was no sign of the boys. It's unknown whether the boys were wearing life jackets.
Though the boys are young, they were legally operating the boat. Florida regulations say a person must be at least 14 to operate a watercraft.
Nearly 50,000 square nautical miles searched
Fedor said the search covered an area just under 50,000 square nautical miles, or 66,200 square miles, a space almost the size of the state of Missouri.
"This was a true all-hands-on-deck effort" involving the Coast Guard, the Bahamas government, and federal, state and local partners, Fedor said.
He said the Coast Guard would reopen the case if new, actionable information about the boys' location comes to light.
People in southeastern Florida rallied around the teens' relatives during the search, including football great Joe Namath, a neighbor of the boys' families. Hundreds of people attended a vigil for the teens Tuesday at the beach in Stuart, a short distance from Jupiter Inlet.
CNN's Ed Payne and Catherine E. Shoichet contributed to this report.