The government made clear any exchange of banking information would de done "case by case" and on the basis of "concrete and justified" requests.
"The private sphere of clients is still protected from unjustified watching from abroad," the statement said.
Jan Rudolph, head of sovereign risk at Global Insight in London, told Al Jazeera that Switzerland was "fully aware" that there is growing international pressure by Western governments on tax havens.
"The governments are under severe pressure themselves because tax revenues are dwindling as each of these economies moves into recession and there is a question of social justice - the idea that everyone should be equal before the law. All residents should pay what is due in terms of tax, so they are clamping down," he said.
"And for the first time we have an alignment of interest - the US, UK, Germany and France. Germany and France have always been pressurising this issue.
"Now we have an alignment; it looks like something could be done. Countries like Switzerland are trying to preempt what policy decisions are likely to come out."
The move comes three weeks before a London summit of leaders from the Group of 20 industrial countries, and in the face of a risk that Switzerland might be included on a so-called blacklist of unco-operative centres sheltering tax evaders.
The Swiss authorities said on Friday that its "banking secrecy does not protect tax crimes".
It also comes after similar decisions by several other European countries. Liechtenstein, Andorra and Belgium have already said they will relax their banking secrecy practices.
On Friday, Josef Proll, the Austrian finance minister, said that his country would agree to lift its banking secrecy, case by case, if "justified suspicions" were presented.
Luca Frieden, Luxembourg's treasury and budget minister, also said on Friday that his country was ready to relax banking secrecy, mainly by accepting to exchange information with other countries if tax fraud were suspected.