The president added that he wanted "a merit based system of immigration and people who will help take our country to the next level" and "safety and security" for Americans.
The president was referring to African countries as well as Haiti and El Salvador during the discussion over bipartisan proposal to restore protections for immigrants.
"This is not a comprehensive immigration reform bill - the president and others yesterday at the White House said that there would be further phases", Goodlatte said in Wednesday's conference.
"I think my positions are going to be what the people in this room come up with", Trump said during a Cabinet Room meeting with a bipartisan group of almost two dozen lawmakers. But conservatives have been pressing him to stand behind their efforts to curtail new immigration.
Congress is grappling with how to break an impasse over the "Dreamers" - immigrants who were brought to the United States illegally as children, but were permitted to stay under Barack Obama's Deferred Action for Childhood Arrivals (DACA) program.
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"We don't want to be basically the bargaining chip to basically tell the president, or even the congress - "do it", you know - and we're giving up this for the community that will get affected", said "Dreamer" Diana Sanchez. This time, they are putting enormous pressure on Democratic lawmakers to shut down the government if DACA is not included in the spending bill.
A thicket of controversial provisions has been under discussion, according to lawmakers, congressional aides and immigration experts outside of government. However, the parents of Dreamers would be able to obtain a three-year, renewable legal status.
The agreement among senators came as more than 100 corporate CEOs urged Congress to "act immediately and pass a permanent bipartisan legislative solution to enable Dreamers who are now living, working, and contributing to our communities to continue doing so".
"It doesn't end chain migration", Cotton said of the bipartisan plan.
His comments drew a chorus of condemnation inside the United States and internationally, especially in Africa.
Alsup, who was nominated to the court by President Bill Clinton, scolded the DHS for having presented no analysis of the impact its order would have on the nearly 700,000 young people "who had come to rely on DACA to live and to work in this country". Alongside it was a document outlining a "vision" for Trump's border wall: 700 miles, at a cost of $18 billion. He also asked Congress to come up with a solution that would codify the program without deporting its beneficiaries, who he called "good, educated and accomplished young people".
In a joint statement after the meeting, the six senators in the Durbin group noted their deal hit those four points and pledged to work to seek support from colleagues, without acknowledging the setback.