Senate Minority Leader Harry M. Reid (D-Nev.) and Sen. Patrick Leahy (D-Vt.), the ranking Democrat on the Senate Judiciary Committee, speak to the media outside the West Wing after this morning’s meeting at the White House. (Yuri Gripas/Reuters)

A White House meeting Tuesday between President Obama and four top senators — Majority Leader Mitch McConnell (R-Ky.), Minority Leader Harry M. Reid (D-Nev.), Judiciary Committee Chairman Charles E. Grassley (Iowa) and the panel’s ranking Democrat, Patrick J. Leahy (Vt.) — did nothing to resolve the standoff over whether to fill the seat of the late Supreme Court Justice Antonin Scalia.

“They were adamant,” Reid told reporters of Republicans’ refusal to hold hearings or offer any potential names for his consideration during what he and Leahy described as a “very short” meeting on the subject. “There wasn’t much said at the meeting.”

“They think they are going to wait and see what President Trump will do I guess as far as the nomination is concerned,” Reid added, referring to Donald Trump, the GOP presidential front-runner. “We are going to continue beating the drums. All we want them to do is fulfill their constitutional duty and do their job. At this phase they have decided not to do that.”

Leahy said that it was the fifth time he had been involved in filling a Supreme Court vacancy and that the current Republican position “makes no sense.”

“Have the hearing. Vote it down. Don’t pretend it doesn’t happen. We have done this a dozen times in presidential election years, had nominations,” Leahy said. “We are sending a signal to our country and to the world that it’s a political institution, and it’s not supposed to be, and it shouldn’t be.”

Neither McConnell nor Grassley — who have said it makes sense to wait for the results of this year’s presidential election before moving forward on a nomination — came out and spoke with reporters immediately after the session, but both shared their thoughts later Tuesday afternoon.

Grassley released a statement calling it a “fair and reasonable approach” to wait until after the elections to act.

“The American people deserve the right to be heard…  They made their voices heard in 2014 when they signaled they wanted a departure from President Obama’s policies by revoking the Democrats’ Senate majority and expanding Republican ranks in the House,” Grassley argued.  Now, with the stakes as high as ever and the political season underway, we should hear from them again.”

Grassley stated that the “executive branch is actively using the judicial branch” to “undermine” democracy.

“Whether everybody in the meeting today wanted to admit it, we all know that considering a nomination in the middle of a heated presidential campaign is bad for the nominee, bad for the court, bad for the process, and ultimately bad for the nation,” he added.

McConnell told reporters in the Capitol that he and Grassley “made it clear that we don’t intend to take up a nominee or to have a hearing,”

“This vacancy will not be filled this year,” he said. “We look forward to the American people deciding who they want to make this appointment through their own votes.”

The Kentucky Republican did the vast majority of talking during the session, according to an individual familiar with the meeting who asked for anonymity in order to speak freely, and no one offered any potential names during the discussion.

White House press secretary Josh Earnest confirmed to reporters that the president solicited names from Grassley and McConnell, but did not comment on their response.

“The president did say that he would take seriously any names that they wanted to put forward,” Earnest said. “If they want to come back to the Oval Office, I am confident we could arrange a meeting.”

Asked about the White House’s next step, Earnest said it would be for the Republicans to continue consulting with the president. “The president’s view of this situation is that any president has a responsibility to consult intensively with Congress.”

Greg Jaffe contributed to this report.