By Ian Simpson

WASHINGTON (Reuters) - Supporters of immigration reform are set to rally at the Capitol on Wednesday to back legislation that would include a path to citizenship for an estimated 11 million undocumented immigrants.

The National Rally for Citizenship, which organizers say will draw tens of thousands of demonstrators, comes after two senior senators said on Sunday that an immigration reform bill would likely be completed in their chamber this week.

Immigration reform has gathered strength in Congress following President Barack Obama's re-election in November. Hispanics, the fastest-growing voter bloc, heavily favored Democrats over Republicans in the elections.

Republicans have since started to get behind immigration reform, an effort that had been mainly embraced by Democrats.

Kica Matos, director of immigration rights at the Center for Community Change, one of the organizers, said demonstrators were being urged to lobby lawmakers before the rally on the Capitol's West Lawn.

"Our concerns really are around making sure that the path to citizenship is clear and expeditious and isn't tethered to anything like enforcement" of border security, she said.

The rally of about 100 organizations is sponsored by immigration reform groups and unions, including the United Auto Workers and the Service Employees International Union.

Immigration legislation in the Democrat-controlled Senate will include an earned pathway to citizenship for undocumented immigrants, bolstered border security and ways for business to meet the need for both high-skilled and low-skilled workers.

A bipartisan group from the Republican-led House of Representatives is working on its own version of a bill that also includes ways to earn citizenship.

The U.S. Chamber of Commerce, the biggest business group, and the AFL-CIO, the largest labor federation, reached an agreement on a guest-worker program in late March. The accord cleared the way for the writing of a full bill in Congress.

If the Senate and House bills pass their respective chambers, they would have to be reconciled before a final version is voted on and then sent to Obama for signing into law.

A bill that gives undocumented immigrants a path to citizenship has a better chance of passing the Democrat-controlled Senate.

It is unclear whether such a bill would pass the House. A number of Republicans there generally support a path to legal status but are reluctant to embrace a plan for citizenship because they say it rewards people who broke the law.

(Reporting by Ian Simpson and Rachelle Younglai; Editing by Cynthia Johnston and Grant McCool)