Story Highlights• NEW: Reid, Pelosi call for "serious negotiations without any preconditions"
• Bush invites lawmakers to discuss impasse on war funding
• President refuses to sign bills that include troop pullout timetable
• Bush: Funds begin running out this month; bipartisan group: Not till summer
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FAIRFAX, Virginia (CNN) -- President Bush on Tuesday invited lawmakers of both parties to the White House to discuss the impasse on funding the Iraq war, as neither side showed signs of backing down.
White House spokeswoman Dana Perino told reporters next week's talks would be discussions and "not a negotiation," while Democratic House and Senate leaders demanded a meeting without "preconditions."
During remarks to members of the American Legion, Bush repeated his threat to veto any bill that includes a timeline for U.S. troops to leave Iraq. He said time is running out. (Watch President Bush say 'the clock is ticking' on war spending bills )
"Instead of approving that vital funding, the Democrat leadership in Congress has spent the past 64 days pushing legislation that would undercut our troops, just as we're beginning to make progress in Baghdad," Bush said.
"The longer Congress delays, the worse the impact on the men and women of the armed forces will be."
The House and Senate have attached language to legislation calling for U.S. combat troops to leave Iraq in 2008 -- the House by the end of August, the Senate by March of that year. (Interactive: Paying for the war)
Answering Bush's invitation with a written statement, Democratic Senate Majority Leader Harry Reid of Nevada, and Democratic House Speaker Nancy Pelosi of California agreed to meet with the president "at any time."
The statement also said "any discussion of an issue as critical as Iraq must be accomplished by conducting serious negotiations without any preconditions. Our goal should be to produce an Iraq supplemental bill that both fully funds our troops and gives them a strategy for success." (Watch Reid say Democrats have previously offered to join talks without preconditions )
The Reid and Pelosi statement accused Bush of "trying to score political points at the expense of our troops." During his remarks, Bush accused congressional Democratic leaders of "using a bill that funds our troops to make a political statement about the war."
Pelosi later said in a news conference in her hometown of San Francisco, California, that Americans want Bush and Congress to work together and "wind down this war."
"What the president invited us to do was to come to his office so that we could accept without any discussion the bill that he wants," she said. "That's not worthy of the concerns of the American people, and I join Sen. Reid in rejecting an invitation of that kind."
Bush said that the Pentagon will have to send to Congress a reprogramming bill that would transfer $1.6 billion from other accounts to cover funding for the war.
Last week, Bush told reporters that without congressional action, the military would begin running short of funds by mid-April. But the bipartisan Congressional Research Service has concluded that the military will have the money to continue fighting through July without additional funding.
By mid-May, Bush said, if funding is not law, problems would grow "more acute," and would include the curtailing of training for active duty forces.
The bill, also sponsored by strong Democratic war critic Sen. Russ Feingold of Wisconsin, would permit spending in only three areas: fighting al Qaeda, training Iraqis and protecting the U.S. Embassy and personnel. The bill is not expected to pass.
At the Pentagon, the Army has warned program managers to prepare for a possible money crunch if Bush vetoes an emergency war spending bill that calls for the eventual withdrawal of combat troops from Iraq. Analysts say Pentagon staff will be the first to face cuts.
The Army Budget Office warned in a memo sent Monday that a resolution to the standoff between the White House and Capitol Hill "is doubtful before the end of April." (Read more about Army preps for a possible wartime money crunch)
As the funding fight continued, war planners were moving forward. On Monday, CNN learned that U.S. commanders in Iraq have asked the Pentagon to extend tours of duty for about 15,000 troops in the war zone by up to four months as part of the U.S. troop "surge" in Iraq that began in January.
Al-Maliki: 'No need' for timetable
Echoing Bush's stance, Iraqi Prime Minister Nuri al-Maliki on Tuesday rejected timetables to determine "departure of international forces" from Iraq.
Al-Maliki told reporters during his visit to Japan that there is progress "on the security issue day by day because we are having security responsibility handed over to us continuously. We see no need for a withdrawal timetable because we are working as fast as we can." (Watch why war supporter GOP Sen. John McCain says 'small progress' is being made in Iraq )
Bombers in Iraq on Tuesday struck a college district and a secondary school in Baghdad and a police recruiting center in Diyala province killing at least 17 people, local authorities told CNN. (Read more about Tuesday's developments in Iraq)
CNN's Suzanne Malveaux and Emily Schultze contributed to this report.
President Bush called on Congress Tuesday to send him a war funding bill without a timetable for troop withdrawal.
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