The Republican-controlled House Transportation Committee voted 33-24 in favor of a bill supporting the Keystone XL pipeline. The measure heads to the full House.
Republican legislators on the House Natural Resources Committee and Energy and Commerce Committee passed similar measures. They say approving the pipeline would ensure U.S. energy security and provide a source of economic stimulus.
The House bills would bypass a State Department review process for cross-border pipelines.
Canadian Prime Minister Stephen Harper was in the United States last week, pressing for the project. He said that, versus rail, pipelines have a better safety record.
Transportation committee member U.S. Rep. Jerrold Nadler, D-N.Y., said the pipeline would push the energy debate in the wrong direction given growing concerns about the environment, however.
"This bill sets a dangerous precedent, undercutting our environmental laws and short circuiting the review process," he said in a statement.
Production of Canadian crude oil, the type designated for Keystone XL, is considered more carbon-intensive than other forms.
Last year was the ninth warmest on record and the 27th consecutive year global temperatures were higher than the 1961-90 average, the World Meteorological Organization reports.