Washington opposes the project in favor of a pipeline planned from Turkmenistan. That project has the support of the Asian Development Bank but would need to pass through Afghanistan.
State Department spokeswoman Victoria Nuland said Zardari's visit was a bad idea.
"This pipeline project would take Pakistan in the wrong direction right at a time that we're trying to work with Pakistan on better, more reliable ways to meet its energy needs," she said.
Nuland expressed doubt whether the pipeline, in the works since the 1990s, would ever develop. If it does go forward, she warned, Pakistan would partaking in sanctionable activity in regards to Iran.
"We've been straight-up with the Pakistanis about these concerns," she said.
She added that the United States was supporting projects that would add 900 megawatts of power to a Pakistani energy grid that can't support the nation's needs.