If Judge Barrett is confirmed, there will be three Justices appointed by Democratic presidents and six by Republicans (including three nominated by Mr Trump).
"This should be a straightforward and prompt confirmation", said the president, while calling for a "respectful and dignified" process for the Supreme Court nominee. "We said that the last time, didn't we", Trump said.
The death of Justice Ginsburg has cleared the way for a 6-3 conservative majority on the nine-member court, which is instrumental in making decisions that influence all corners of American life.
"Judges are not policymakers", she said.
Democrats oppose moving forward with a vote on Ginsburg's replacement so close to the election, citing Senate Majority Leader Mitch McConnell's decision in 2016 to block then-US President Barack Obama's Supreme Court nominee because it was an election year, which all but ensures a fierce confirmation battle on Capitol Hill in the coming weeks.
Barrett used her own remarks at the White House to try and calm the waters.
Joe Biden has criticised the choice of Amy Coney Barrett as a Supreme Court justice. A deeply conservative Catholic and mother of seven, she is an opponent of abortion, a core issue for many Republicans. "She not only broke glass ceilings, she smashed them".
While Democrats appear powerless to stop Barrett's confirmation in the GOP-controlled Senate, they are seeking to use the process to weaken Trump's reelection chances.
Meanwhile, Barrett's fellow professor at the University of Notre Dame, O Carter Snead, wrote in The Washington Post that "liberals have nothing to fear" with the conservative jurist.
Senate Judiciary Committee hearings to consider Barrett's nomination are scheduled to begin October 12.
Barrett's critics have been quick to point out her conservative views on abortion and healthcare, for starters, while her defenders are hailing her as a brilliant legal mind who has strong connections to her faith and family. "We move forward on this nomination knowing that the President has picked a highly qualified individual who will serve our nation well on the highest court in the land".
It is also possible the court will be asked to settle disputes arising from the presidential election on the 9 November.
Increases in mail, absentee and early voting brought about by the coronavirus pandemic have already led to a flurry of election litigation, and both Trump and Biden have assembled armies of lawyers to continue the fight once vote-counting begins. The national party, in concert with President Donald Trump's campaign, is planning local events and protests across the country to support Barrett's confirmation as well.