Trump said he not will push the candidates to say whether they would overturn the 1973 Roe v. Wade decision, which established a woman's right to abortion.
He said one or two court prospects would likely come to his club in Bedminster, in New Jersey "just for an interview" over the weekend, and that he anticipated interviewing "six or seven" candidates altogether.
"If we put another two or perhaps three justices on, that's really what's going to be, that's what will happen", Trump said at the final presidential debate in October 2016.
Trump says he thinks that is "inappropriate to discuss".
"It's a great group of intellectual talent".
Trump's first Supreme Court pick, made after Senate Republicans blocked President Barack Obama's pick to fill a Supreme Court vacancy, was Neil Gorsuch, who has been a reliable conservative vote.
Democrats argued the move would follow the precedent taken by Senate Republicans in 2016, when McConnell refused to consider a Supreme Court nominee until after the presidential election. Flake told The Arizona Republic he would make a determination on voting for Trump's nominee after reviewing the pick.
West Virginia Senator Joe Manchin says it would be tough to support someone who would revamp the landmark decision.
A person familiar with the process said White House officials are focused primarily on five federal appeals court judges - Brett Kavanaugh, Amy Coney Barrett, Thomas Hardiman, Raymond Kethledge and Amul Thapar - all Republican appointees with conservative track records.
A Republican involved in Senate races said Democrats will have to choose between a base that wants a big fight against Trump's nominee and moderate voters in their states. The Judiciary Committee does not have any Democrats who look as if they may jump ship and vote with Republicans on Trump's nominee. "I think that's one thing (that) energizes conservatives more than anything else, is the Supreme Court". Recent history suggests that, as with the brief government shutdown over the Deferred Action for Childhood Arrivals program earlier this year, Senate Democrats might not have the stomach for that brand of politics.
U.S. President Donald Trump waves as he walks on the South Lawn of the White House upon his return from Mount Pleasant, Wisconsin, to Washington, U.S., June 28, 2018.
"On the left, that's what they're concerned about", Perino said.
When asked whether USA sanctions on Russian Federation might be lifted, he said: "We'll see what Russian Federation does".
On Thursday, Trump brought Murkowski and five other senators to the White House to discuss the vacancy.
Both sides are gearing up for a confirmation battle in the Senate after Trump names his nominee.