WASHINGTON — House and Senate negotiators announced an agreement Monday on legislation that would allocate about $17 billion to overhaul the Department of Veterans Affairs’ sprawling and beleaguered health care system. But the deal does not give the department everything that officials there have said is needed to fix its problems.

The agreement set off a frantic rush on Capitol Hill to gather signatures from members of the conference committee working on the bill so that it could be put to a vote of the full House and Senate before lawmakers adjourn for an August recess on Friday.

If approved, the legislation would end a sometimes rancorous standoff over how much to spend to begin to fix the department, and it would help ensure that veterans who face long waits to see doctors at the department’s facilities could get appointments more quickly with private physicians. A few details were still being worked out even after the chairmen of the House and Senate Veterans Affairs Committees announced the agreement Monday at an afternoon news conference.