WASHINGTON — President Trump announced on Tuesday that he had signed a sweeping executive order to eliminate and streamline some permitting regulations and to speed construction of roads, bridges and pipelines, declaring that the moves would fix a “badly broken” infrastructure system in America and bring manufacturing jobs back to the country.

In an explosive news conference overshadowed by questions about his response to a white nationalist rally over the weekend in Charlottesville, Va., Mr. Trump tried several times to steer the conversation back to infrastructure.

The president has vowed to pass a $1 trillion package to revitalize the nation’s infrastructure, but so far no such legislation exists. Mr. Trump said he was not worried about his chances of winning support for his plan, even in the wake of a failed effort to overhaul health care.

“We will end up getting health care, but we’ll get the infrastructure, and actually infrastructure is something that I think we’ll have bipartisan support on,” Mr. Trump said. “I actually think Democrats will go along with the infrastructure.”