Pelosi, D-Calif., said it would be unconstitutional to rescind birthright citizenship through an executive order.
He said: "You can definitely do it with an act of Congress".
Politics or not, immigration lawyers say no president can unilaterally end citizenship rights for children of non-citizens who are born on US soil.
The 14th Amendment allows for "all persons born or naturalised in the U.S., and subject to the jurisdiction thereof, are citizens of the USA and of the State wherein they reside".
The move, which many legal experts say contradicts the Constitution, would be the boldest yet by a president elected to office pledging to take a hard line on immigration, an issue he has revived before next week's midterm elections. "It's ridiculous. It's ridiculous".
The revoking of birthright citizenship was on Trump's agenda also while he was campaigning for the presidential election.
Mr Trump would also need backing from three quarters of USA state legislature at a constitutional convention - a gathering with the intent of altering the constitution.
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"But the Supreme Court of the U.S. has never ruled on whether or not the language of the 14th amendment, subject to the jurisdiction thereof, applies specifically to people who are in the country illegally", Pence said.
But Trump told Axios he didn't think he needed to go about ending the practice with a constitutional amendment. Mr Trump has long-criticised so-called "anchor babies", a phrase used to describe the practice in which undocumented immigrants are able to gain legal foothold in the country through their citizen children.
His comment comes as a massive wave of immigrants from some Latin American countries traverse through Mexico to reach the U.S. border, where Trump's administration has deployed 5,200 troops to stop the immigrants from entering the country.
Trump, should he pursue the executive order, would face court challenges, and it remains unclear whether he could prevail.
An executive order is "in the process"..
With that said, Yegani is skeptical as to whether Trump will actually move forward with this plan. We're not catching, we're not releasing.
What does the end of birthright citizenship mean? "The 14th Amendment's citizenship guarantee is clear".