They had to orbit the Earth 34 times before their rendezvous with the international space laboratory, instead of the fast-track route of four orbits originally envisaged.
-, NASA TV/AFP
This still image from a NASA video shows the Soyuz TMA-12M spacecraft, a few meters away from docking to the International Space Station (ISS), on March 27, 2014
"It was a long two days but we made it. Glad to be here," Swanson said on a video link-up from the ISS.
The issue arose once their Soyuz capsule was in orbit and a thruster failed to fire to assist its approach for docking with the ISS.
US space agency NASA said in a statement that the Soyuz spacecraft "was unable to complete its third thruster burn to fine-tune its approach" to the ISS.
The Soyuz capsule later carried out three manoeuvres in orbit bringing it on the correct trajectory.
The head of the Russian state firm Energia that supplies the Soyuz rocket that propels the craft into space said Wednesday that the origin of the problem was not yet clear.
"It could be mathematics, it could be a transmitter problem or that the engine choked. But most likely it was a mathematical problem," said Vitaly Lopota, quoted by the Interfax news agency.
This would imply that ground scientists failed to work out the correct altitude in orbit for the thruster to fire to take the Soyuz to the ISS.
A commission has been formed to pinpoint the cause of the problem.
- Fast-track route to continue -
Vasily Maximov, AFP
Russian Soyuz-FG rocket with the Soyuz TMA-12M spacecraft and a crew of US astronaut Steven Swanson, Russian cosmonauts Alexander Skvortsov and Oleg Artemyev aboard, blasts off from the Baikonur cosmodrome in Kazakhstan, early on March 26, 2014
The flight director for the Russian section of the ISS, Vladimir Solovyov, vowed Friday that Russia would continue to use the fast-track route to the ISS that it began using last year.
"We will continue to work according to this scheme. You can't scare us off with just this one thing," he said, cited by the ITAR-TASS news agency.
Mission control "at a certain moment did not receive the necessary orientation" from the Soyuz, he said.
"This was the rarest combination of circumstances," Solovyov said, while adding the Soyuz's onboard computers may be updated as a precaution.
"Maybe for such an unlikely case, we will put something extra into the memory of the onboard computer -- just in case."
After the retirement of the US shuttle, NASA is for now wholly reliant on Russia for delivering astronauts to the space station.
The trio bring the ISS crew up to six by joining incumbent crew Koichi Wakata of Japan, American Rick Mastracchio and Russian Mikhail Tyurin, who are due to leave in May.
- US-Russia space cooperation -
Space officials have made clear that space cooperation will continue unaffected by the mounting diplomatic strains that have seen the US impose sanctions on Russian officials over Moscow's annexation of Crimea.
Skvortsov and Swanson said at a pre-flight news conference that they had decided to have dinners together on board the ISS "as an opportunity to come together as friends in the kitchen and look each other in the eye".
"I think we will all be able to live peacefully together," Skvortsov said.
47-year-old Skvortsov is making his second space flight and 53-year-old Swanson, a veteran of two past shuttle missions, his third.
43-year-old Artemyev meanwhile is on his first voyage to space. He took part in a 2009 experiment where volunteers were shut up in a capsule at a Moscow laboratory for 105 days to simulate the effects of a possible voyage to Mars.