DENVER – Buoyed by a powerful debate showing, Mitt Romney said Thursday he offers “prosperity that comes through freedom” to a country struggling to shed a weak economy. President Barack Obama accused the former Massachusetts governor of running from his own record in pursuit of political power.

Both men unleashed new attack ads in the battleground states in a race with little more than a month to run, Obama suggesting Romney couldn’t be trusted with the presidency, and the Republican accusing the president of backing a large tax increase on the middle class.

Not even Democrats disputed that Romney was likely to benefit politically from the debate Wednesday night in which he aggressively challenged Obama’s stewardship of the economy and said his own plans would help pull the country out of a slow-growth rut. Still, there was no immediate indication that the race would expand beyond the nine battleground states where the rivals and their running mates spend nearly all of their campaign time and advertising dollars.