The problem arose in a fund which covers liabilities that arose before the city’s 900 manual services staff transferred in 2000 to contractor City Care.
This contract ends in 2010 and the council must settle its pension liabilities before it is retendered.
Executive member for corporate services Alan Waters (Lab) said: “We are going through the retendering so the pension obligations have to be sorted out.
“Things were fine when I took a report to council last March that said we owed£1.8m, but since then it has ballooned to£19m as a direct result of stock market conditions.”
Cllr Waters said he would either have to convince the council pensions committee to spread the£19m liability over 20 years, or else try to borrow the money from the government.
“It would be very difficult to find that money otherwise,” he said.
“It is a disgrace that the very poor judgment of the financial services industry and banks have been allowed to create a situation where there are knock-on effects like this.”