Some Republicans open to meeting Garland include incumbent senators set for a tough re-election, such as Illinois Sen. Mark S. Kirk and New Hampshire Sen. Kelly Ayotte, who said she still opposes a confirmation vote.
"I feel I would want to explain my position to the nominee," Ayotte said, The New York Times reported. "He does serve on the Circuit Court of Appeals, so I want to give him that courtesy."
Kirk and Maine Sen. Susan Collins are the only two Republican senators who have broken away from party stance and said they are willing to vote for a Supreme Court nominee. Arizona Sen. Jeff Flake has also said he would meet with Garland.
"This is a distinguished jurist who has been on the court for 19 years and his record deserves scrutiny," Collins told reporters, adding that Sen. Majority Leader Mitch McConnell "believes strongly that this decision should be made by the next president ... I don't agree with that decision, but I respect it."
McConnell on Wednesday called Garland to explain that he will not meet with him because there would be no action over his nomination.
"Rather than put Judge Garland through more unnecessary political routines orchestrated by the White House, the leader decided it would be more considerate of the nominee's time to speak with him today by phone," Don Stewart, McConnell's spokesman, said.
On Wednesday, President Barack Obama urged senate leadership to work to hold a confirmation vote. Garland received positive bipartisan support when he was confirmed to his seat on the U.S. Court of Appeals for the D.C. District with a 76 to 23 vote.
Republican leaders argue that with upcoming general elections and less than a year remaining in his second term, leaving Scalia's seat vacant for the new president to fill is the right move.