WASHINGTON — A peacemaking summit meeting between Republican lawmakers and their renegade presidential nominee, Donald J. Trump, descended on Thursday into an extraordinary series of acrid exchanges, punctuated by Mr. Trump’s threatening one Republican senator and deriding another as a “loser.”

Mr. Trump arrived in the capital with hopes of courting skeptical House and Senate Republicans and mending his relationship with Senator Ted Cruz, his former rival for the nomination, in a blitz of face-to-face meetings. But the friendly atmosphere turned fraught when Mr. Trump lashed out in the face of direct criticism.

The tension reflects the lingering fissures in a Republican Party that continues to grapple with Mr. Trump as its standard-bearer, and underscores Mr. Trump’s limitations when it comes to unifying the party and moving beyond political grudges.

He has disappointed some members of the party who have hoped his campaign would become more disciplined, but instead have seen him dwell on and even repeat his own missteps rather than maintaining a focused offensive against Hillary Clinton.