(CNN)A new national poll shows Hillary Clinton carrying a six-point lead over Donald Trump with both presidential primaries now in the rearview mirror, though both major party presumptive nominees remain challenged by controversies weighing on their campaigns.
Poll: Clinton leads Trump
According to a CBS poll released Thursday, Clinton leads Trump 43% to 37% -- numbers that are down significantly for both candidates from a couple months ago, when they garnered closer to 50% and 40%, respectively.
Clinton's advantage remains when Libertarian presidential nominee Gary Johnson is included. In that scenario, Clinton draws 39% support to 32% for Trump and 11% for Johnson.
The poll, which was mostly conducted before the Orlando terror attack, also asked voters on their view of the candidates' ability to manage terrorism and national security. Clinton received the edge on this issue, with 50% saying she would do a better job than Trump at 43%.
Voters expressed significant disapproval of Clinton's use of a private email server and Trump's ethnicity-based attacks on the federal judge overseeing the Trump University lawsuit.
Two-thirds of voters said they think Clinton "did something wrong" in using a personal email server while secretary of state -- though opinions are sharply divided along party lines. And 7-in-10 voters said that Trump's comments about the Trump University judge were offensive and 42% think Trump either did something improper or illegal related to the now-defunct program.
Voters favored Clinton on handling an international crisis and say she is prepared for the job of president while Trump got high marks on saying what he believes, according to the poll. But both candidates are viewed as dishonest and face questions about their judgment.
The CBS poll was conducted June 9 through June 13 among 1,280 adults nationwide, including 1,048 registered voters. The margin of error is plus or minus 3 points.