“I only worry for the country in that Hillary Clinton was careless and negligent in allowing Weiner to have such close proximity to highly classified information,” Mr. Trump said, using language that echoed criticism of Mrs. Clinton this summer by the F.B.I. director, James B. Comey Jr. “Who knows what he learned and who he told? It’s just another example of Hillary Clinton’s bad judgment. It is possible that our country and its security have been greatly compromised by this.”

A spokesman for Mrs. Clinton, Nick Merrill, declined to comment on Mr. Trump’s remarks.

The spotlight on Ms. Abedin and her proximity to Mrs. Clinton has been an increasing distraction for the campaign.

Several of Ms. Abedin’s emails on Mrs. Clinton’s private server have drawn scrutiny amid accusations that donors to the Clinton Foundation received special access to the State Department.

And political opponents, including Senator Charles E. Grassley, Republican of Iowa and chairman of the Judiciary Committee, have questioned Ms. Abedin’s arrangement to earn income privately while she worked for Mrs. Clinton at the State Department. In addition to being on Mrs. Clinton’s personal payroll, Ms. Abedin received money from the Clinton Foundation and Teneo, a consulting firm founded in part by Douglas J. Band, previously a senior aide to Mr. Clinton.

Ms. Abedin, 40, has been at Mrs. Clinton’s side since she was an intern to the first lady in the 1990s. Now vice chairwoman of the Clinton campaign, Ms. Abedin, often described as a surrogate daughter, occupies an almost singular role as a trusted, and visible, confidante to Mrs. Clinton.

Their lives took similar tracks, as both women, citing their religious beliefs, seemed determined to remain married despite their husbands’ sexual proclivities.

Image Huma Abedin and Anthony Weiner at the Met Gala in May. Credit... Timothy A. Clary/Agence France-Presse — Getty Images

Mrs. Clinton strongly supported Ms. Abedin when Mr. Weiner’s sexually charged text messages came to light in 2011, a year into their marriage, and again in 2013, when Mr. Weiner was running for mayor of New York. Friends of Mrs. Clinton said that she had spoken to Ms. Abedin at length about the marriage and that she supported Ms. Abedin’s decision to remain with Mr. Weiner and work on their relationship.