WASHINGTON—Congressional leaders have reached an agreement on a new stopgap spending bill that would extend government funding into March, according to a person familiar with the matter, as House Speaker Mike Johnson (R., La.) sticks to his plan to defy the most brass-knuckled budget hawks in his party in a bid to avoid a government shutdown.

The government has been running on short-term spending laws since the start of the fiscal year on Oct. 1, as lawmakers continued to negotiate full-year funding.