British Divers Marine Life Rescue said 18 of the animals were floated back out to sea at about 04:00 on Tuesday. Two more were later floated.
However, several of the whales then stranded on the shores of nearby Staffin Island.
It was understood that eight of the whales have died and nine remain stranded on the small island.
The coastguard said it could be high tide at 19:00 before those animals could be pushed back into open water.
It was believed the stranding was caused by a female whale getting into difficulty while calving. The calf died.
Hebridean Whale and Dolphin Trust raised the alarm after seeing whales in distress on Monday afternoon.
Environment Secretary Richard Lochhead said the Scottish government was offering assistance to the effort to save the whales.
He said: "I am very concerned to hear about this stranding of pilot whales on Skye.
"Marine Scotland and British Divers Marine Life Rescue are currently working hard to alleviate the situation.
"We have a patrol vessel and other staff on-site and I am being kept informed of the situation.
"Sadly it appears that some of the whales have already died and the situation is becoming increasingly difficult as the outgoing tide is leaving the stranded animals out of the water."

Aaron Lennon is still missing but Muhamed Besic is nearing a first-team return following nine months out with a serious knee injury.
Burnley midfielder Steven Defour is fit, having played only twice in 10 weeks because of various injuries.
Johann Berg Gudmundsson has stepped up his recovery from knee ligament damage but might not be risked.
Guy Mowbray: "Everton are hunting a new club record for successive Premier League home wins, against a Burnley side still seeking ANY away win.
"The Clarets have three chances left, with the last (and furthest!) trip to Bournemouth probably their best bet - assuming both are safe from relegation by the season's penultimate weekend.
"With one win in nine since January, it's testament to how well Burnley did earlier in the season that they'll surely be okay by then.
"The FA Cup semi-finals line-up should mean that Everton are sitting pretty for a Europa League place, and whilst a strong finish won't get them in the top four it might prove key to keeping Romelu Lukaku."
Twitter: @Guymowbray
Everton manager Ronald Koeman on his players' ambitions: "If you ask the players one by one, everyone will mention they like to play Champions League: for every manager, for every player and also the fans.
"Our next step is to play in Europe. It will be difficult but if we finish fifth or sixth it would be perfect as you don't play any qualification games for the Europa League."
Burnley manager Sean Dyche on Michael Keane's PFA Young Player of the Year nomination: "It's a great sign for him and he deserves to be in that company.
"We're not shining lights of the Premier League or a superpower, so for other players to see that and say 'hang on a minute, he's been terrific in a smaller side at a smaller club' is good, it's good of his peers to recognise that.
"He's in some very good company, some players who are having absolutely fine seasons, and he's having a very strong season too."
Since suffering their only home league defeat of the season, against Liverpool in December, the Toffees have won seven league games in a row at Goodison Park.
I think Everton's excellent run will continue - and maybe Ross Barkley will deliver the knock-out blow.
Prediction: 2-0
Lawro's full predictions v singer Sting
Head-to-head
Everton
Burnley
SAM (Sports Analytics Machine) is a super-computer created by @ProfIanMcHale at the University of Salford that is used to predict the outcome of football matches.
Rescuers have gone to the aid of 21 long-finned pilot whales which stranded on the shore at Staffin on Skye.
[NEXT_CONCEPT]
Everton defender Ashley Williams returns from suspension for the visit of Burnley on Saturday.