The company behind the Keystone XL pipeline on Monday asked the U.S. government to suspend its permit application, throwing the politically fraught project into an indefinite state of limbo, likely beyond the 2016 U.S. elections.

In a letter, TransCanada Corp. asked the State Department, which reviews cross-border pipelines, to suspend its application while the company goes through a state review process in Nebraska it had previously resisted. The move comes in the face of an expected rejection by the Obama administration...