LONDON (Reuters) - British Prime Minister Gordon Brown said on Tuesday banks must be made to act responsibly but that a levy on transactions was only one possible way of achieving this.

Brown floated, to a weekend meeting of G20 finance ministers, a series of ways of getting banks to start repaying some of the enormous cash injections they have received over the last year and build up funds to deal with future bailouts.

The US and Canada, however, both voiced strong opposition to one of the ideas — a tax on financial transactions that has already been championed by Germany and France. Some British newspapers have judged that a defeat for Brown.

"I think if you read my speech on Saturday, what I was talking about was the social responsibility of financial institutions," Brown said at his regular news conference.

"And we've found also that in good times the banks achieve very high rewards and in bad times it has been the country, the nation's taxpayers as a whole, who have had to underpin the banking system," he added.

Britain has pumped billions of pounds into bailing out Royal Bank of Scotland and Lloyds Banking Group.

Brown's calls for banks to give something back chime with comments from France and Germany, but the idea of a transaction levy has long been opposed by the United States.

"There should be a debate about a new contract between banks and the society they serve, it will have to be a debate conducted at a global level," Brown added.

"I mentioned four possible ways that we could do it — an insurance levy, a resolution fund, contingent capital liabilities or a global levy."

"I don't think this debate can be avoided. I think this debate is fundamental to the future of banking."