But he was quickly rebuffed by Mrs. Clinton, who declared on Twitter that she was uninterested in Mr. Koch's support.

In an interview with Jonathan Karl of ABC, which aired on "This Week with George Stephanopoulos," Mr. Koch sounded at times baffled and disappointed by the language and ideas of several Republican presidential candidates.

He called a plan by Donald J. Trump to temporarily bar Muslims from entering the country "monstrous" and dismissed Senator Ted Cruz's proposal to carpet-bomb territory held by the Islamic State as "frightening" hyperbole.

Mr. Koch spoke somewhat fondly of former President Bill Clinton, suggesting he held down government spending and regulation compared with his successor, President George W. Bush. He called Mr. Bush "a fine person, and tried to do the right thing but was misguided."

That prompted a question about Mrs. Clinton. Below is a transcript of the ensuing exchange: