Gov. Robert F. McDonnell’s gifts scandal has pulled his job approval rating to a new low, according to a Quinnipiac University poll released Wednesday morning.

The survey found that 46 percent of registered voters approve of the job McDonnell is doing and 37 percent disapprove. That’s a dip from the 49 percent approval rating he had in Quinnipiac’s May 15 poll, and down sharply from highs the term-limited Republican once enjoyed as one of the nation’s most popular governors.

“The lofty levels of 2-1 job approval that Virginia Gov. Bob McDonnell once enjoyed have slipped away with six months left in his term,” said Peter Brown, assistant director of the Quinnipiac University Polling Institute. “He’s under 50 percent for the second poll in a row, with just a 9-point net approval after substantial media coverage of his relationship with a campaign donor and associated problems.”

State and federal authorities are investigating McDonnell’s relationship to Star Scientific Inc. chief executive Jonnie R. Williams Sr. The Washington Post reported in late March that McDonnell and first lady Maureen McDonnell had taken steps to promote Star’s nutritional supplement, Anatabloc, and that Williams had paid the $15,000 catering tab at the June 2011 wedding of their daughter Cailin.

The governor has said their efforts to boost the product were consistent with what he and the first lady have done to promote myriad Virginia-based businesses. He also said he did not have to disclose the wedding payment because it was a gift to his daughter, not him.

Voters have become more aware and concerned about the scandal as more details have emerged, the poll found.

Quinnipiac’s May 15 poll, conducted within two weeks of the first reports about the wedding payment, found that 44 percent of voters thought McDonnell’s ties to Williams were “just politics” rather than a “major issue.” In the May 15 poll, 59 percent of Virginians said McDonnell has “high personal moral and ethical standards,” while 16 percent said he does not, and 25 percent said they were unsure.

Since that time, The Post has reported that federal and state investigators are looking into other large payments or loans from Williams, including $70,000 to a real estate corporation owned by the governor and his sister, $50,000 to Maureen McDonnell and $10,000 for the May wedding of another daughter, Jeanine. They are also investigating luxury gifts from Williams, including a $6,500 Rolex watch for the governor and a $15,000 New York shopping spree for the first lady.

Now, 41 percent of voters are not satisfied with the way the governor is handling the controversy, the poll found. Twenty-seven percent consider McDonnell’s behavior to be serious wrong-doing and 5 percent say it is not serious; 16 percent say he is not involved in any wrong-doing, while 49 percent saying they haven’t heard enough to know, the poll found.

Forty-four percent of Virginians think the governor is honest and trustworthy, the most recent survey said.

The poll also found that 60 percent of voters believe McDonnell shares the same level of honesty and integrity as most people in public life. Just 16 percent of voters say McDonnell should resign.

“Almost 80 percent of voters are aware of the controversy and seem to be somewhat concerned,” Brown said. “The bottom line seems to be that they view him as just another politician, but at this point they are not clamoring for his scalp.”

Quinnipiac surveyed 1,030 registered voters on land lines and cellphones from July 11 to 15 for its poll, which has a margin of error of plus or minus 3.1 percentage points.