ATLANTA, Georgia – Delta Air Lines Inc. posted its strongest increase in traffic yet during the ongoing rebound last month, driven by a surge in international travel, as it increased flight capacity and flew fuller airplanes.

Separately, Republic Airways Holdings Inc.'s (RJET) discount Frontier airline saw a 15% jump in traffic as its capacity increased 10% and its load factor--a measure of plane fullness--hit 91%. That was a record for a fourth-straight month and compares with 87% a year earlier.

About a year ago, Republic was in the process of working out a deal with Frontier's creditors to take over the company as it emerged from bankruptcy court. Its plan beat out Southwest Airlines Co.'s bid in a bankruptcy auction last August.

Most US airlines are reporting growing increases in traffic as travelers return to flying. Airlines had been cutting capacity in recent years, first in response to record-high fuel prices and then to cope with a deep drop in demand during the recession.

Delta's traffic has switched back and forth between growth and decline over the last couple of months, but June's 4.2% increase in traffic builds upon May's 2.7% increase. Its traffic was driven by an 8.8% jump in international traffic. Travel overseas was one of the hardest-hit segments for air carriers during the recession. Delta's domestic traffic was up 1.2% in June.

Overall, Delta's capacity also rose 1.5%, while its load factor increased to 87.7% from 85.5%.

In May, Continental Airlines Inc. (CAL) and UAL Corp.'s United unveiled a $3 billion merger proposal that would vault them over Delta to become the world's biggest airline.