The Russian president later congratulated the engineers after the fault was rectified and the rocket launched
President Vladimir Putin told space engineers to get their act together after he flew thousands of kilometres to watch the inaugural launch of a rocket from a new spaceport, only for it to be postponed in the final seconds.
The fault was discovered with the unmanned Soyuz on Wednesday - a minute and a half before it was due to lift off - but it eventually launched in the early hours of Thursday.
The Russian president revealed his displeasure at the initial failure after meeting officials at the Vostochny Cosmodrome.
"The fact is there is a large number of hitches. That is bad. There should be an appropriate reaction," he said sternly.
Mr Putin said the technical glitch was to do with the rocket system, not the launch pad, and that Russia still led the world in many aspects of space technology.
The Soyuz later launched and a statement confirmed all three satellites has successfully been put into orbit.
The president struck a different tone after the problem was rectified, telling the team: "I want to congratulate you.
"We can be proud. Yesterday the technical side was put to the test and the launch had to be stopped, but it happens. It's a normal thing."
However, he added that if suspects in a criminal investigation into embezzlement on the project were found guilty "they will have to swap their warm bed at home for a prison bunk".
The spaceport, the first civilian rocket launch site on Russian territory, has been built in the remote Amur region near Russia's border with China.
It is the flagship project in a $52bn (€45.7bn) investment in space exploration up to 2020 and was built to replace Russia's reliance on the Baikonur Cosmodrome leased from Kazakhstan.
However, it has been beset by problems, with various people under suspicion of corruption, workers striking over pay, overrunning costs and a delay last year to its scheduled completion date.
Problems with Russian space rockets are not just a concern for the Russians, but the Americans too.
Since the retirement of the space shuttle programme, NASA depends on Russia to fly its astronauts to the International Space Station.