Monday’s poll conducted by the Swiss finance ministry showed 58 percent of respondents support the system.
The poll was published as the Swiss authorities re-launched a campaign to clean up the country's international reputation, arguing that Switzerland is not an offshore centre and is not an ideal place to hide illegal funds.
Switzerland's Finance Minister Kaspar Villiger highlighted tougher regulation in recent years but also urged the country's banking industry to provide both "top quality performance and ethics".
"These are not contradictions but challenges which Switzerland and the Swiss financial sector must face and which indeed they are willing to face," he said in a statement published with the survey.
Although the overall level of support for the country's unique confidentiality laws was largely stable, the poll indicated that a growing proportion of Swiss would like to see secrecy softened to allow tax evasion to be detected.
About 27% of those polled said it should be possible to lift banking secrecy in cases of tax evasion, against 25% in the same poll in 2001, the finance ministry said in a statement.
Eleven percent felt that banking secrecy should be abolished.
New crime-busting laws in the 1990s forced a softening of banking secrecy, obliging banks to identify customers and allowing full access to banking records for investigators fighting organised crime, money laundering and tax fraud.
US, EU to blame
Critics of those laws blame powerful US politicians such as former New York Senator Alfonse for spearheading campaigns on behalf of American Jewish groups against the Swiss banking system.
But the laws still protect account holders from having their financial affairs revealed to tax authorities at home or abroad in cases of tax evasion.
Switzerland has come under intense pressure to abolish banking secrecy in recent years, more recently from neighbouring countries that fear they are losing millions of euros in revenue because Swiss secrecy acts as a magnet for tax evaders.
Last month, Switzerland and the 15 EU countries reached a tentative agreement on a compromise, levying a tax on EU citizen's investment income to discourage tax evaders.
Sixty-seven percent of the 1500 people polled in April and May rejected the idea of a partial lifting of banking secrecy for foreigners.
While an Italian tax amnesty last year brought about 30 billion euros ($28 billion) back into Italy – more than half of it from Swiss bank accounts according to the Italian authorities – Villiger is considering an amnesty for Swiss taxpayers.
A similar amnesty in 1969 brought 11.5 billion Swiss francs ($8.4 billion) in undeclared funds back into Switzerland's own tax system.