"I think every little bridge-building exercise like that is very helpful," Cornyn said on Tuesday, characterizing the meeting between Pence and Senate Republicans.
Cornyn signaled that many members of the caucus were supportive of Pence, who served six terms in Congress, and welcomed the opportunity to "reconnect with an old colleague."
"Most of us were reassured when Mr. Trump picked him for vice president," Cornyn added.
On Tuesday, Trump’s running mate sat down with House Republicans in the morning and Senators in the afternoon. According to media reports, Pence is expected to participate in major fundraiser later in the day at the Capitol Hill Club in Washington, DC.
Trump, the billionaire turned presidential candidate, initially alienated many in the Republican establishment with his unconventional campaign, but has increasingly sought to unify the party ahead of the November 8 election.