Helicopters are dropping food, torches and satellite phones onto the crippled cruise ship, the Costa Allegra, as the vessel is being slowly towed towards the main Seychelles Island.
The boat "is coming slowly, but is coming", a Seychelles coast guard official, who declined to be named, told the AFP news agency on Wednesday from the organisation's command centre in Victoria port.
The liner was expected to arrive into port in Mahe, the main island of the Seychelles archipelago, on Thursday, he added.
Footage shot from the rescuing helicopter showed people crowded around one of the cruise ship's swimming pools.
More than 1,000 passengers and crew spent the night in the dark and without air-conditioning after a fire in the engine room blacked out the ship.
Italian coastguard and government inspectors are also on their way there. They will investigate what went wrong, a month after the sinking of its sister ship, the Costa Concordia, near the Italian island of Giglio.
A French tuna fishing boat, the Trevignon, responded to the Costa Allegra's mayday call and was towing the boat solo, crawling along at a speed of around six knots (11km per hour) through calm seas.
Al Jazeera's Sue Turton, reporting from Mahe, said: "One of the biggest concerns is safety of the vessel. This is very much [a] pirate area."
Pirates, based off the coast of Somalia, have been active in the Indian Ocean and Arabian Sea over the last several years.
French marines are on board the fishing trawler, and armed guards are also present on board the cruise ship, Turton reported. The Seychelles coast guard will also be protecting the two vessels.
"Helicopters are supplying, what they are calling 'comfort items', like telephones and flash lights," our correspondent said.
"The biggest worry here on the island is: do they have enough hotel beds to house the more than 1,000 people on board."
Monday's fire aboard the 188-metre Costa Allegra occurred only six weeks after the Costa Concordia accident that left dozens dead and another seven still remain missing. Both ships are operated by Costa Crociere SpA, which is owned by the Florida-based Carnival Corp.
Officials said the blaze was extinguished without causing any injuries, and that the vessel was stable and upright.
The luxury ship was sailing about 320km southwest of the Seychelles when the fire broke out and it sent a distress signal, the company said.
A spokesman for Costa said the passengers included 130 each from Italy and France, 100 from Austria and 90 from Switzerland.
The 28,597-tonne Costa Allegra left northern Madagascar, off Africa's southeast coast, on Saturday and was cruising towards Victoria. Costa said the Allegra had been due in Victoria on Tuesday.