The rocket was carrying a weather satellite and other equipment took off in the Amur region near the Chinese border.
Russian space agency Roscosmos said on Tuesday it had failed to establish contact with a newly launched weather satellite.
Roscosmos said the satellite had not reached its designated orbit, and that it could not make contact with it. Roscosmos experts were analysing the situation, it said in a statement.
The rocket was launched from its new Vostochny cosmodrome in the far east on Tuesday, as Moscow seeks to ease dependence on Baikonur in Kazakhstan.
Marking another milestone after the inaugural lift-off last year, the Soyuz rocket carrying a weather satellite and other equipment took off at 0541 GMT (2:41pm local time) as scheduled.
"All the initial stages of the rocket's flight went according to plan," the Russian space agency Roscosmos said in a statement.
National television broadcast live footage of the launch, showing the rocket taking off into a grey sky in the Amur region near the Chinese border.
Apart from the Meteor weather satellite, the rocket carried 18 payloads from institutions and companies in Canada, the United States, Japan, Germany, Sweden and Norway, the space agency said.
Prime Minister Dmitry Medvedev said Monday that such contracts would help Russia modernise its space industry.
"The launch of foreign devices with the help of Russian launch vehicles should strengthen our positions on the global market of space services and increase the volume of extra-budgetary funds and investments," Medvedev told a meeting.
More launches to come
The first launch from Vostochny spaceport in far eastern Russia took place in April 2016, with President Vladimir Putin overseeing the take-off.
That launch was a major milestone for the country's beleaguered space sector, with the new cosmodrome touted to mark a rebirth of an industry plagued by a string of embarrassments in recent years.
The third launch from Vostochny is scheduled for December 22.
"The programme of launches will continue next year – it will grow, increase," Deputy Prime Minister Dmitry Rogozin, who oversees space, told Medvedev on Monday.
The Kremlin's goal is to ease Russia's dependence on Baikonur in Kazakhstan, a launchpad Moscow has been forced to rent since the collapse of the Soviet Union.
Russia is also home to the Plesetsk cosmodrome in the north, which is used for satellite launches and missile testing.
But Vostochny, like Baikonur, is closer to the equator, making launches cheaper and more energy efficient.
The new cosmodrome currently has one launchpad for the Soyuz, the only rocket currently being used for manned space flights.
Rogozin said he planned to chair a meeting at the launchpad set to address a second construction phase that will see the country build a reinforced launchpad for the new Angara rocket.
The launch of the Angara, which is being tested to replace the ageing Proton workhorse rockets, is scheduled for 2021.
Construction on the new spaceport began in 2012 but has been marred by labour disputes, corruption scandals and delays.
The first satellite launch had been scheduled for late 2015, but setbacks forced authorities to review the timetable.
In October, Russia launched from Plesetsk a European satellite dedicated to monitoring the earth's atmosphere, the protective layer that shields the planet from the sun's radiation.