WASHINGTON, Jan 11 (Reuters) - The Republican-led U.S. House of Representatives committee overseeing an effort to impeach Homeland Security Secretary Alejandro Mayorkas over illegal immigration on Wednesday brushed aside the border chief's offer to testify in his defense.

The committee said in a press release that Mayorkas had refused to testify in recent months despite "repeated invitations" and that it would move ahead with a hearing next week featuring "victims of Secretary Mayorkas’ border crisis."

The response came after the U.S. Department of Homeland Security (DHS) sent a letter to the committee saying Mayorkas was willing to discuss possible dates to testify.

Republicans have increasingly focused on illegal immigration, an animating issue for their base voters, in the run-up to Nov. 5 elections that will decide control of the White House and Congress. The party kicked off impeachment proceedings against Mayorkas on Wednesday during a hearing where they blamed him for record levels of migrants attempting to illegally cross the U.S.-Mexico border.

Democrats dismissed the hearing as political theater and said Republicans should instead pass a White House proposal that would provide some $14 billion for border management.

The only secretary ever to be impeached was former President Ulysses S. Grant's secretary of war William Belknap in 1876 following allegations of corruption. On Wednesday, a law professor and impeachment expert testified that Republicans had not presented evidence that Mayorkas had committed an impeachable offense.

The DHS letter to the committee noted that Mayorkas will meet with top Mexican officials next week to discuss border security, suggesting he may not be available to testify at the planned Jan. 18 hearing.

The panel's Republican chairman Mark Green slammed the DHS letter and meeting with Mexican officials in a statement.

"Apparently, accountability and transparency are not high on his priority list," Green said. (Reporting by Ted Hesson; Editing by Scott Malone and Alistair Bell)