BERN/ZURICH (Reuters) - Switzerland's parliament halted a bill on Wednesday that would let Swiss banks hand over client information to the U.S. authorities as part of a clampdown on tax evasion, saying it needed to know more about what the deal involved.

The Swiss government wants parliament to rush through the legislation this month to put an end to a long-running tax spat with U.S. authorities over banks accused of helping wealthy Americans hide their money from the tax man.

The lower house backed a motion from the left-wing Social Democrats (SP) to put the bill on ice.

But it rejected demands from the right-wing Swiss People's Party (SVP), the biggest party in parliament, to take the bill entirely off the summer session agenda, meaning it could still be debated in coming weeks.

The Swiss government has warned that U.S. authorities could bring more criminal charges against its large banks if parliament does not act quickly.

A spokesman for Switzerland's finance ministry declined to comment on Wednesday's decision.

The Swiss government has been negotiating with U.S. authorities for two years to try to resolve the tax dispute, but abandoned an attempt to reach an umbrella settlement deal for the whole financial industry due to secrecy laws as well as squabbling among the country's banks as to who should pay what.

The bill now before parliament would not provide the names and account details of the Swiss banks' clients but would allow the sharing of information on their behavior.

Switzerland's tradition of banking secrecy has helped make it the world's biggest offshore financial center, with $2 trillion in assets. But it has come under fire during the global financial crisis, as governments clamp down on tax evasion, with German and French authorities also investigating Swiss banks.

(Reporting by Ruben Sprich and Katharina Bart, Writing by Caroline Copley, Editing by Gareth Jones)