Trump also said the issue would ultimately be decided by the Supreme Court.
Trump is seeking to end the long-standing right to US citizenship for children born to non-citizens in the United States, a policy that he said in his tweets "costs our Country billions of dollars and is very unfair to our citizens".
Yesterday, leading Democrats and immigrants rights activists blasted Trump's pledge to issue an Executive Order, and Ryan dismissed the idea during a radio interview, saying it is not consistent with the 14th Amendment of the Constitution.
Senate Judiciary Committee Chairman Charles Grassley, (R), said the issue is one on which Congress, rather than the president, should take the lead.
In his tweet today, Trump asserted that birthright citizenship is not subject to the 14th Amendment because of the inclusion of the phrase "subject to the jurisdiction thereof".
Legal experts have debated for years how to interpret the citizenship clause of the 14th Amendment, but the consensus is one-sided: Most agree that it in fact grants citizenship to those born on US soil.
The first section of the amendment says: "All persons born or naturalised in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside."
Some legal scholars argue that the phrase "and subject to the jurisdiction thereof" seems to give the government some leeway to restrict the right, just as other constitutional principles can be limited.
But the mainstream opinion from both right and left is that it is more likely that a constitutional amendment, rather than federal legislation or an Executive Order, would be needed to change the birthright conferred on people born here.