Swiss lawmakers threw their support behind a tax proposal which could help to strike a deal with the United States on Wednesday, a move which is seen as instrumental to settling a U.S. probe into Swiss banks with hidden offshore accounts.

The proposal, which clarifies how Switzerland would hand over data on Americans suspected of dodging taxes at home, seeks to backstop an expected deal over U.S. probes into 11 banks including Credit Suisse and Julius Baer, likely to comprise a data handover and fine payment.

An overwhelming majority of Switzerland's lower house backed the proposal, dismissing minority motions seeking to sink the plan. The lawmakers tabled the formal vote to Monday as debate on the proposal extended well into the evening.

Left-wing lawmakers backed the plan, swung by clean-money measures for Switzerland unveiled by Swiss finance minister Eveline Widmer-Schlumpf last week.

The tax plan, defended by Widmer-Schlumpf in parliament on Wednesday, garnered enough support from other parties to expect to pass the formal vote on Monday despite right-wing opposition. Switzerland's upper house already passed the plan in December.

The Swiss government is eager to avoid a repeat of UBS, when legal loopholes threatened to derail a deal reached with U.S. officials over hidden offshore accounts that bank offered wealthy Americans.

The plan, criticized in parliament on Wednesday by detractors including influential former Swiss cabinet member Christoph Blocher, represents a weakening of Switzerland's long-cherished secrecy laws, which have underpinned the country's finance industry, on which the economy relies heavily.

Provided the proposal passes Monday's vote and a 100-day waiting period without a call for a referendum, attention will shift to talks between the U.S. and Switzerland for a deal meant to sweep Swiss bank accounts clean of offenders and make good on past transgressions.

According to a source familiar with the matter, Swiss and U.S. talks are continuing, but sticking points remain in the deal's details.

(Reporting By Katharina Bart; Editing by Elaine Hardcastle and Jon Loades-Carter)