* Senate bill calls for insurance market overhaul

* Leaves blank details of proposed government health plan

* Obama promises Medicare and Medicaid savings (Adds new material throughout)

By Donna Smith

WASHINGTON, June 9 (Reuters) - Leading Senate Democrats unveiled on Tuesday a plan to reshape U.S. healthcare that calls for sweeping insurance market reforms and prohibits insurers from denying coverage or charging more due to medical history.

The measure also would require individuals to buy insurance, provide subsidies to help make coverage affordable and set up a new government plan to help provide medical coverage for the uninsured.

The Senate Health, Education, Labor and Pensions Committee's bill is one of at least three healthcare proposals brewing in Congress, which Democrats hope will lead to legislation that President Barack Obama can sign into law by October.

"Our goal is to strengthen what works and fix what doesn't," Senator Edward Kennedy, chairman of the committee, said in a statement that accompanied the bill's unveiling.

Democrats in the U.S. House of Representatives and a second group of U.S. senators led by Senate Finance Committee Chairman Max Baucus are developing similar proposals. Baucus has been working with Kennedy's panel and is expected to unveil his version of the bill in the coming days.