ROME (Reuters) - The Italian government may have to inject capital directly into weaker banks to bolster their financial strength, a government source said on Thursday, adding it was waiting for the results of stress tests being conducted by European banking authorities.

The results of the tests are expected to be published at the beginning of the third quarter.

The source told Reuters the government was also working on a plan to increase the firepower of bank bailout funds Atlante, which was set up in April to help lenders raise cash and sell bad loans, by 3-5 billion euros ($3.34-5.57 billion) by the summer.

The source said the government was in talks with private pension funds to seek additional contributions for Atlante. Other contributions were expected to come from the state lender Cassa Depositi e Prestiti and from a public company called Societa per la Gestione di Attivita (SGA).

(Reporting by Giuseppe Fonte; editing by Silvia Aloisi)