WASHINGTON—A group of Democratic senators urged Republicans to come to the negotiating table to work out a broad immigration and border security plan, pushing an unlikely alternative path as the GOP-controlled Congress prepared to pass a bill designed to speed up deportations and President Trump moved ahead with his own crackdown.

The senators said they would cooperate with the GOP to address "pressing border security and immigration needs”

Border state Sen. Mark Kelly (D-AZ) and a dozen other primarily Democratic senators are pushing the Republican-controlled Senate to include them in their work addressing the border and immigration matters.