By Laurence Norman and Frances Robinson

BRUSSELS--The two Belgian financial firms that failed the European Central Bank and European Banking Authority stress tests said they had no need to raise further capital as a result of the outcome.

The country's banks could survive tough shocks but need to continue improving their capital position, National Bank of Belgium Governor Luc Coene said following the results.

"Even in tough conditions Belgian banks would be resilient, and capable of absorbing the shocks," Mr Coene told reporters. "Still, it's not the moment to put down tools and say 'it's all fixed there's nothing more to do,' there's a need to strengthen the capital position and equity ratios."

Belgium's AXA Bank Europe said Sunday it had carried out a 225-million-euro ($285 million) capital injection last month which addressed its capital shortfall.

The bank failed the adverse-scenario ECB stress test, with the ECB saying it would have a 3.4% Common Equity Tier 1 capital ratio in the adverse scenario in 2016, well below the 5.5% required.

However the bank said that last month its parent company injected EUR135 million in common equity Tier 1 capital and a EUR90 million intragroup Contingent Convertible bond, which addressed its capital needs.

"AXA Group (AXAHY) has anticipated the outcome of the adverse macro scenario of the ECB stress test by providing the necessary capital resources for AXA Bank Europe to comply with the ECB" requirements, the bank said in a press release.

The bank said "no additional measures to strengthen the solvency position" of AXA Bank Europe are required and that, following the capital injection, it has overall Tier 1 capital of EUR992 million and a forecast Tier 1 capital ratio of 20.8% as of Sept. 30.

AXA also said two legacy portfolios had a significant impact on the stress test result--a structured-bonds portfolio which the bank has been running down since 2008 and was completely sold last month; and a mortgage-credit portfolio in Hungary which the bank has been running down since 2011.

Dexia SA (DEXB), the other Belgian bank that failed the adverse scenario of the stress test, said that no remedial action or state aid was required by the ECB and the EBA after the test. Dexia is being wound down under a resolution plan approved by European Union authorities in 2012.

The bank said it had already boosted its EUR195 million common equity Tier 1 capital by asset sales in the first three quarters of this year. It also said the adverse scenario test didn't take into account the benefits of a measure granted on the valuation of its sovereign securities holdings.

The ECB and the EBA confirmed Sunday that taking into account the orderly resolution plan of Dexia, which benefits from a government guarantee, there is no need for the bank to raise further capital.

"Dexia couldn't survive it were a regular bank, but it's not a normal bank, it's a bank in resolution," Mr. Coene told reporters. "The stress test validates this approach, there are many long years ahead of dismantling Dexia piece by piece."

Dexia said in a statement that the difference between the amount provisioned by Dexia for credit risk and the result of the asset quality review is EUR 79.05 million, and that its collective provisions were "deemed sufficient."

Mr. Coene said this wasn't a concern, and that Dexia's main problem wasn't the actual assets, but the length of time they need to be held for: from 20-50 years. With the state guarantee, "they have enough resources to absorb all the other elements," he added.

Write to Laurence Norman at laurence.norman@wsj.com and Frances Robinson at frances.robinson@wsj.com

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