Donald Trump rails against criticism of his immigration policies

Donald Trump got back to touting his proposed immigration policies in a series of tweets Saturday night - the same day he pulled back on his original calls for blanket bans on Muslim immigration to the US.

The presumptive Republican presidential nominee said "We must suspend immigration from regions linked with terrorism until a proven vetting method is in place."

He also insisted that he only wants to admit "those who love our people and support our values."

Earlier Saturday, CNN reporter Jeremy Diamond, tweeted that Trump spokeswoman Hope Hicks clarified that he does not support banning all foreign Muslims - just those from "terror states."

The clarification comes after the businessman was hit hard by Democrats and his own party for comments he has made suggesting that mass deportations were needed in order to keep America safe.

Trump backed away from the term "mass deportation," but only so much:

The GOP candidate's latest proposals come in the wake of the Orlando nightclub massacre, in which 49 people were killed by a New York-born man whose parents are from Afghanistan.

Trump points to the killings - the worst on US soil since the September 11 attacks - as proof that his proposals to keep some Muslims out of the US are necessary. He had words about President Barack Obama, too:

Obama, growing increasingly exasperated with Trump's rhetoric, tore into him last week, saying "We don't have time for charlatans, and we don't have time for hatred, and we don't have time for bigotry."

"We don't have time for just popping off and saying just whatever comes to the top of our heads," Obama added.