(Releads, updates with Pelosi, Reid statement)

WASHINGTON, April 11 (Reuters) - Congressional Democratic leaders agreed to meet with U.S. President George W. Bush at the White House next week after a face-off over a $100 billion Iraq war spending request degenerated on Wednesday into bickering over where, when and whether to meet.

Bush invited the Democratic and Republican leaders of the Senate and the House of Representatives to come to the White House next Wednesday to talk about the money. But he refused to negotiate a troop pullout timetable Democrats have attached to the war funds.

Senate Majority Leader Harry Reid and House Speaker Nancy Pelosi said in a joint statement, issued after the White House rejected an invitation to meet lawmakers this week on Capitol Hill, they would attend.

"We will be at the White House on Wednesday to talk with the president. We will listen to his position, but in return we will insist that he listen to concerns of the American people that his policies in Iraq have failed and we need to change course," the statement said.

Reid's office had earlier turned the tables by inviting Bush to go to Capitol Hill on Friday to discuss the funding request with him and other Democratic leaders and some Republican senators.

"Rather than wait until next week to meet as you proposed, we would like to begin this dialogue now," they wrote to the president.

The idea for the meeting was "to begin bridging the differences between your Iraq policy and that supported by the Congress late last month," they wrote.

After the letter was sent, Reid told reporters a trip to Capitol Hill could be invigorating for Bush. "The president is as isolated, I believe, on the Iraq issue as Richard Nixon was when he was hunkered down in the White House," Reid said.

The White House quickly rejected the request and stuck to its plans to meet next week with whoever shows up.

"The president of the United States and the commander in chief of our troops yesterday invited the bicameral, bipartisan leadership of the United States Congress to come and discuss with him the path to getting a clean bill to his desk to fund the troops," Perino said.

"There is a meeting on the president's schedule next Wednesday, and he looks forward to meeting with those who attend," she added.

Bush has threatened to veto the bills passed in the House and Senate that attach a pullout timetable to the funding request: a Sept. 1, 2008, deadline in the House bill and a goal of March 31, 2008, in the Senate legislation. A veto of the legislation, however, means no funds for the troops and Congress would have to take up a new bill.

Democrats say they were elected to control of Congress last November on a mandate to change the strategy in Iraq.

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