WASHINGTON — A dispute between Democrats and the White House over how to handle coronavirus testing emerged on Monday as one of the most significant sticking points as negotiators struggled to finalize a nearly $500 billion bipartisan agreement to replenish a loan program for small businesses and provide more funding for hospitals and testing.

Democrats are pushing to include a requirement in the measure, which is likely to include $25 billion for testing, that the Trump administration establish a national testing strategy, a move the president and Republicans have resisted, insisting on leaving those decisions to each state.

The impasse hindering the latest round of federal aid to respond to the coronavirus pandemic reflects a broader disagreement over how to handle testing, a crucial element of the government response on which the Trump administration has been roundly criticized for falling short. President Trump and members of his team have boasted repeatedly about the amount of testing available and pressured governors to accelerate testing in their states. Governors have repeatedly appealed for more federal funding and other help — or, in the case of Gov. Larry Hogan of Maryland, taken matters into their own hands and negotiated with suppliers on their own to obtain test kits.

Democrats argue that a national testing strategy is crucial to combating the spread of the coronavirus and allowing states to plan for eventual reopening. But Republicans, wary of placing the political onus on the administration to devise and implement such a strategy, have argued that states should set their own plans.