Perry Cohen and Austin Stephanos, both 14, were last seen on Friday afternoon buying $110 worth of fuel near Jupiter, before setting off on a 19-foot boat.
Their capsized boat was found on Sunday morning more than 180 miles from where they set off two days before.
"I just want him home. I know he's coming home," said Austin's mother Carly Black on NBC's Today programme.
Pamela Cohen, mother of Perry, told NBC that she believes her son and his friend "are doing everything they can to stay afloat".
She said the two boys have worked with boats their whole lives and that it is natural for them to be on the water.
The two mothers said the boys went fishing offshore when the weather turned and "something went amiss".
The US Coast Guard expanded its search on Tuesday morning, searching up to Georgia and down to Cape Canaveral in Florida through the day and night.
A spokesman said they were still optimistic they can be found alive.
They were last seen buying petrol and authorities said they may have been headed toward the Bahamas.
Nick Korniloff says his stepson, Perry, and Austin were were supposed to stay on a nearby river and waterway when they set out to go fishing on Friday, but they ended up in dangerous waters.
Former American football player Joe Namath, Ms Cohen's neighbour, has offered a $100,000 (Â£64,100) reward for information on the missing boys.
Mr Namath said during a press conference "We've got to believe in their wherewithal".

Dzhokhar Tsarnaev, 21, is charged with 30 counts related to the bombings, which killed three people and wounded more than 260 in April 2013.
As part of the prosecution's summing up, medical examiners gave graphic details of the injuries suffered by those who died in the attack.
Mr Tsarnaev could face the death penalty if found guilty.
Massachusetts Chief Medical Examiner Henry Nields testified that the youngest victim of the attacks, eight-year-old Martin Richard, received injuries to every part of his body.
The testimony was illustrated by autopsy photos and the child's bloody, torn clothing.
Mr Nields said one piece of shrapnel appeared to have gone straight through Richard's body.
"It would be difficult to say the precise location due to the size of the openings in the abdomen," he testified, according to Reuters.
The defence began calling its own witnesses later on Monday.
Earlier in the trial, the defence made the surprise admission that Mr Tsarnaev had participated in the attacks.
But defence lawyers argue that his 26-year-old brother, Tamerlan, had been the driving force behind the attacks. By doing so they hope to spare their client the death penalty.
Mr Tsarnaev is charged with 30 counts related to the bombings. The brothers set off a pair of homemade pressure-cooker bombs at the race's crowded finish line.
Mr Tsarnaev is also accused of fatally shooting a police officer three days later.
The prosecution says Mr Tsarnaev, who emigrated with his family from Chechnya, had extremist views and wanted to hit back at the US in revenge for military action in Muslim countries.
Authorities are continuing to search for two teenagers who went missing while fishing off the Florida coast.
[NEXT_CONCEPT]
The prosecution has rested its case in the trial of a man accused of carrying out the 2013 Boston Marathon bombings.