US President Donald Trump urged the Senate's Republican leader on Wednesday to resort to the "nuclear option" of scrapping longstanding chamber rules if needed to confirm Supreme Court nominee Neil Gorsuch, an aggressive opening to what's shaping up as a ferocious clash over the future of the high court.

At the White House a day after nominating Gorsuch, Trump endorsed a scenario that would involve majority Republicans unilaterally changing Senate rules over the objections of the Democratic minority.

It could come into play if Democrats try to block Gorsuch's confirmation with a filibuster, as the liberal base is demanding, and would allow the GOP to confirm Gorsuch with a simple majority instead of the 60 votes now needed.

Addressing GOP Senate leader Mitch McConnell from the White House, Trump said, "If we end up with that gridlock I would say, 'If you can, Mitch, go nuclear.'" He said of Gorsuch that it "would be an absolute shame if a man of this quality was caught up in the web."

Trump made his comments as Gorsuch traversed Capitol Hill, escorted by Vice-President Mike Pence and winning extravagant praise from Republican senators.

Democratic divisions were on display. Minority Leader Chuck Schumer faced intense opposition from base voters to Trump's nominee, while political risks confronted a half-dozen Democratic senators representing red states who are up for re-election next year and may feel pressure to support Gorsuch.

"The president made an outstanding appointment; we're all thrilled and looking forward to getting the confirmation process started," McConnell said as he stood with a smiling Gorsuch in the senator's ceremonial office in the Capitol.

McConnell has not said whether he might invoke the nuclear option if minority Democrats block Gorsuch's confirmation, but the Senate leader has said repeatedly that, one way or another, Gorsuch will be confirmed. He reiterated that Wednesday evening in an interview on WHAS radio in Kentucky, saying: "Well I appreciate the president's advice. What I would say to him is what I would say to you: We're going to get this nominee confirmed and this is the beginning of a lengthy process."

Schumer said that "this Supreme Court will be tried in ways that few courts have been tested since the earliest days of the Republic."