(Changes sourcing to text of the proposal, adds airline shares)

WASHINGTON/CHICAGO, Sept 8 (Reuters) - A fresh U.S. Senate Republican coronavirus spending package introduced on Tuesday does not include new government assistance for U.S. airlines or airports, a text of the proposal showed, as the sector races to save jobs before October.

More than 35,000 workers at two of the largest U.S. carriers alone - American Airlines and United Airlines - are set to lose their jobs once an initial $25 billion in payroll support from the government expires this month.

That has fueled a furious push by unions for a six-month extension of the aid, with flight attendants and other aviation workers planning to march outside the U.S. Capitol on Wednesday.

Last month a group of Senate Republicans backed extending $25 billion in payroll assistance for airlines, an idea Democrats also support.

That proposal was excluded from the latest Senate measure, which was reviewed by Reuters and is expected to be voted on Thursday, but it is an opening salvo for talks that are expected to intensify once the U.S. House returns from recess next week.

The Senate proposal also excludes $10 billion in assistance for airports that was part of an earlier Senate bill.

Republicans and Democrats have been jockeying for months over the next phase of coronavirus aid, after passing more than $3 trillion this year.

U.S. President Donald Trump has floated the idea of airline aid without congressional action, but officials said last week the administration has yet to settle on an approach.

One possibility under discussion was redirecting unspent funds from the Coronavirus Aid, Relief, and Economic Security (CARES) Act passed in March, people familiar with the matter said, though it was unclear how conditions could be set without going through Congress.

The initial $25 billion airline payroll aid included restrictions on share buybacks and executive compensation and required airlines to protect jobs and pay through September.

Airlines are bracing for a slow recovery from the coronavirus pandemic but say they need trained workers ready to service and fuel any economic rebound. (Reporting by David Shepardson and Tracy Rucinski; Editing by Richard Chang)