Shortly after she ended the phone call, Sunderland, who left California on her 36-foot (11-metre) sailboat Wild Eyes in January, activated two emergency beacons but has otherwise not been heard from since, ABC reported.
During a blog entry written on Wednesday, Sunderland said she had spent several days in rough weather and had to patch one of her sails. Sunderland also wrote that she was having trouble with her Internet system.
Sunderland had hoped to become the youngest sailor to circumnavigate the globe alone nonstop but had to give up her chance at that record when she was forced to pull into a port at Cape Town, South Africa, for repairs to her boat.
Laurence said his daughter had all of the safety equipment she needed, including a cold water survival suit, life raft and bag with emergency supplies.
"If she can keep warm and hang on, help will be there as soon as possible," he said.
The Australian Maritime Safety Authority said an airliner with 11 trained observers on board would try to make contact with Sunderland's yacht from high-level, and then descend to make visual contact if necessary.
Under French rescue co-ordination, a fishing boat would be on scene on Saturday afternoon, joined on Sunday morning by a French Fisheries Patrol vessel and a third ship on Sunday evening.
The area is one of the most difficult parts of the world to launch rescue operations. British solo sailor Tony Bullimore had to be rescued by an Australian navy frigate in 1996 after his yacht capsized during a race in which another competitor died.