It also offered up four other general principles it wants to see in an immigration bill. These include reforms to address backlogs in the immigration process, reforms that are "consistent with civil, constitutional and basic human rights," a commitment to support civic and economic engagement by immigrants, and "smart, effective and humane enforcement measures" at the border.
Rep. Ileana Ros-Lehtinen (R-Fla.), one of the leaders of the caucus, said an immigration bill supporting these principles would be "consistent with our American principles."
"We are a nation of laws, and we are also a nation based on opportunity and fairness for all," she said. "I am hopeful that my colleagues in the House can keep these principles in mind as we work together to honor the rule of law and strengthen our families and our communities."
Another caucus leader, Rep. Eliot Engel (D-N.Y.), called on the House to move legislation that creates some way for illegal residents to win legal status.
"We cannot ignore the 11 million people – and their families, which include American citizens –living in our country," he said. "Fixing this situation will strengthen our national security, aid our economy, and end the exploitation of millions of people."
But despite these calls, House GOP leaders continue to insist that the House will do its own immigration bills, and have not said they would pursue any bill creating a pathway toward legal status. Over the weekend, House Speaker John BoehnerJohn BoehnerBoehner returns to the spotlight Cruz confronts Trump supporter Graham: 'Lucifer may be the only person Trump can beat in a general election' MORE (R-Ohio) declined to say whether the House would consider the idea, and immigration bills that have moved so far deal mostly with enforcement and visas for high-skilled workers.