"Were dysfunction in this market to continue or worsen, there would be a material risk to UK financial stability," the BoE warned.
One source at the Treasury said Kwarteng would not resign, and the government would not reverse its policy.
A second person familiar with the situation said Truss still backed Kwarteng and they would announce further economic reforms soon.
One source at the meeting said Kwarteng had asked the assembled finance bosses what they could do to calm markets.
U.S. bond giant PIMCO said it would have less confidence in sterling than it did before last Friday's announcement.