The Trans-Pacific Partnership (TPP), a wide-ranging proposed trade agreement that could include more than 10 countries including Australia, has faced another test in the US Senate as legislation needed to close the deal returned for a second run through the chamber.

The legislation for US president Barack Obama's signature trade agreement has already endured six weeks of congressional wrangling and two close brushes with failure after revolts by Mr Obama's own Democrats, many of whom believe trade deals will threaten US jobs.

The bill, which would establish a fast track through Congress for trade deals, needs support from 60 senators to clear a procedural hurdle.

Although the measure passed the Senate a month ago on a vote of 62-37, including backing from 14 Democrats, some may withdraw support.

Fast-track legislation gives lawmakers the right to set negotiating objectives for trade deals, such as the 12-nation TPP, but restricts them to a yes-or-no vote on the final agreement.

Trading partners say they want fast-track legislation enacted before finalising the TPP, which would be the biggest trade deal since the North American Free Trade Agreement liberalised commerce between the United States, Canada and Mexico two decades ago.

Republicans want measures passed by end of the week

It took two attempts to pass this same procedural hurdle on the legislation's first run through the Senate last month, after Democrats successfully demanded the measure be bundled with three other trade bills.

Opposition in the House of Representatives, where Democrats refused to renew a previously uncontroversial program providing aid to workers hurt by trade, has forced the measures apart again.

Senators will vote Tuesday (local time) on limiting debate on fast track and — if that vote succeeds — on the actual bill on Wednesday, before tackling a second bill extending trade benefits to African nations.

That bill now also contains the worker aid program.

Republicans want both measures to pass this week before Congress goes on a week-long break so that Mr Obama can promptly sign them into law.

"If we simply vote the same way we did a couple of weeks ago, we won't miss this opportunity," Senate majority leader Mitch McConnell said.

The top Democrat on the Senate finance committee, Ron Wyden, backed the plan but several others would not reveal their stances to reporters as unions intensified their opposition campaign.

The TPP, a potential legacy-defining agreement for Mr Obama, would open markets for US exporters like Intel Corp and Caterpillar Inc, extend monopoly periods for Pfizer Inc and rivals' medicines and cut import costs for companies like Wal-Mart Stores Inc.

Reuters