Originally slated to fly in the small hours of Saturday morning, the Parker Solar Probe blasted off Sunday from Florida's Kennedy Space Center at 03:31 am EDT / 00:31 PT / 8.31 UMT.
The problem on Saturday had to do with the gaseous helium pressure alarm on the spacecraft, officials said early Saturday.
The car-sized spacecraft will travel directly into the Sun's atmosphere, about four million miles from its surface - and more than seven times closer than any spacecraft has come before, thanks to its innovative Thermal Protection System.
A NASA spacecraft has taken off on an historic mission towards the Sun in a delayed launch at Cape Canaveral in Florida.
Over the next seven years, there will be 24 close approaches to the sun.
The entire project cost R20.5-billion and will continue until 2025.
In particular, it is hoped to give scientists a greater understanding of solar wind storms that have the potential to knock out the power on Earth.
More knowledge of solar wind and space storms will also help protect future deep space explorers as they journey toward the Moon or Mars.
Parker Solar Probe spacecraft was launched on Sunday. We are ready. We have the ideal payload.
The tools on board will measure the expanding corona and continually flowing atmosphere known as the solar wind, which solar physicist Eugene Parker first described in 1958. The extreme pull of the sun's gravity will then accelerate the probe up to insane speeds of as much as 430,000 miles per hour (700,000 km/h) as it grazes the edge of the most powerful object in our corner of the galaxy.
Parker said he was "impressed" by the Parker Solar Probe, calling it "a very complex machine".
Scientists have wanted to build a spacecraft like this for more than 60 years, but only in recent years did the heat shield technology advance enough to be capable of protecting sensitive instruments.
"We'll also be the fastest human-made object ever, travelling around the Sun at speeds of up to 690,000km/h (430,000mph) - NY to Tokyo in under a minute!" she told BBC News.