By Jason Douglas 

Bank of England Gov. Mark Carney on Wednesday urged eurozone officials to foster stronger growth in the currency union by deepening the fiscal ties between member states.

His unusually forthright remarks underscore the frustration of British policy makers at the slow pace of reform in the U.K.'s biggest export market.

During a speech in Dublin honoring former Canadian Finance Minister Jim Flaherty, who died last year, Mr Carney said European monetary union wouldn't be complete until member countries build mechanisms to share fiscal risks.

Mr. Carney, who is also a Canadian, served alongside Mr. Flaherty as governor of Canada's central bank until joining the BOE in 2013.

Successful currency unions such as Canada, the U.S. and the U.K. have arrangements in place to channel public funds to areas of hardship from well-off regions whenever needed, he said. The eurozone doesn't.

"Europe's leaders do not currently foresee fiscal union as part of monetary union. Such timidity has costs," said Mr. Carney, according to a text of his speech.

His remarks come at a fraught time for the eurozone.

Sunday's election victory in Greece of the antiausterity Syriza party threatens to reignite the region's debt crisis and undermine a fitful global recovery.

The European Central Bank, faced with the threat of a prolonged period of falling prices in the 19-nation currency area, this month unveiled a huge program of asset purchases to spur growth and stoke inflation.

The ECB's actions were "timely and welcome," Mr. Carney said. But he warned that feeble growth risks increasing the debt burden of deeply indebted nations and that the "fear of stagnation" is holding back spending and investment. He said efforts to create a banking and capital markets union in the eurozone to channel private-sector savings easily across borders are welcome but don't go far enough.

"For complete solutions to both current and potential future problems the sharing of fiscal risks is required," Mr. Carney said. Options for sharing such risks range from outright cash transfers to struggling regions from the union's prosperous core to a eurozone-wide employment insurance program, he said. "Without this fiscal risk-sharing, the eurozone finds itself in an odd position."

Mr. Carney's remarks highlight British unease at the eurozone's ongoing economic malaise, which officials blame for stymieing U.K. exports and hammering business and consumer confidence. After a painful recession in 2008 and 2009, followed by several years of weak growth, the U.K. grew 2.6% in 2014, according to official data, its fastest pace in seven years.

Mr. Carney didn't discuss the outlook for U.K. monetary policy at length in his remarks, beyond reiterating that with inflation subdued, future increases in interest rates are likely to be gradual and limited.

Write to Jason Douglas at jason.douglas@wsj.com