The British government owns part of the Russian space agency, but it won't be able to launch them without assurances they won't be used for military purposes.
A rocket carrying satellites for OneWeb is going to be launched on Friday.
OneWeb had two days to provide legally binding guarantees.
OneWeb hasn't commented yet.
The UK government is under pressure to pull the launch over the Russian invasion of Ukraine.
OneWeb was bought out of bankruptcy in 2020 by the UK taxpayers.
In an interview with Russia 24 TV channel, Mr Rogozin said that OneWeb and its partner Arianespace had been contacted by the government of Russia to demand comprehensive legally binding guarantees that the satellites would not be used for military purposes.
The satellites will be sent to the assembly and test building if we don't receive confirmation by 2 o'clock on March 4.
The launch is scheduled to take place on Friday at 22:41 local time.
The OneWeb contract was paid in full and the funds would not be returned, according to Mr. Rogozin.
We received all the money for the manufacture of launch vehicles, upper-stages and the necessary launch services.
The money will stay in Russia because of the aggressive policy of the West and the sanctions against Russia, according to the boss of the company.
The space agency demanded that the UK government withdraw its stake in the company.
The UK government will not be selling its holding at the request of Moscow. British taxpayers took a share in the company after it went bankrupt, and the talk has been about adding defence and security capabilities to future OneWeb satellites.
There is an emerging challenge for authoritarian regimes. It is much harder to control the flow of information with space infrastructure than it is with terrestrial networks.
The number of satellites in the new constellations makes them hard to jam.
Ukrainians will be able to use Musk's Starlink broadband system after he shipped antenna terminals to the country.
Most of the country is too far south for OneWeb to work at the moment. The future launches planned by OneWeb have filled the gap.
The situation in Ukraine was in the mind of the man who persuaded Boris Johnson to buy into OneWeb.
There are just a few launches left to complete OneWeb's network of 648 satellites.
Russian Soyuz vehicles are scheduled to fly out of Baikonur in the coming months and all of the missions are booked on them.
The company can deliver broadband internet connections to locations above 50 degrees North, but it needs more satellites if it wants to run a truly global service.
The rest of Europe, most of the US, Africa and Asia would not be included.
The chair of the Commons business committee wrote to the science and space minister to call off the launch. He said it was not appropriate after Russia invaded Ukraine.
It is right for questions to be raised about future space cooperation with Russia following the illegal invasion of Ukraine, according to a UK government spokesman. We are monitoring the situation closely and engaging regularly with our partners.