Paul Manafort, Mr. Trump’s campaign chairman, on Sunday played down the troubles that Mr. Trump has caused for himself recently with comments at his rallies and interviews, including his attacks on a Gold Star family and his surprising decision to withhold endorsements from Speaker Paul D. Ryan and Senator John McCain for several days last week.

Mr. Manafort said on Fox’s “Sunday Morning Futures” that the general election was just starting and that Mr. Trump would focus on attacking Mrs. Clinton starting on Monday with an economic speech in Detroit.

“The campaign is a three-month campaign — we’re at the beginning,” Mr. Manafort said. “Starting Monday, we’re going to be announcing our economic plan. When we do that, we’re comfortable that we can get the agenda and the narrative of the campaign back on where it belongs, which is comparing the tepid economy under Obama and Clinton versus the kind of growth economy that Mr. Trump wants to build.”

Perhaps Mr. Kaine’s most surprising comments were about the fate of Judge Garland. He and Mrs. Clinton strongly support Judge Garland’s nomination to the Supreme Court, but the judge’s future remains unclear in the Republican-controlled Senate. If the Senate does not act on Judge Garland, and Mrs. Clinton becomes president in January, she would have to decide whether to stick with the choice of Mr. Obama, her close ally, or to pick someone else for the vacancy.

Mr. Kaine, who represents Virginia in the Senate, said the fate of Judge Garland “will be for the president and the president-elect to decide,” adding that it was up to Republicans in control of the Senate to bring the nomination to a vote. Asked if it was a 100 percent certainty that Mrs. Clinton would stick with Judge Garland’s nomination if she were elected, Mr. Kaine sidestepped the question and said that the onus was on Republicans to hold a vote and that he would vote in favor of the nomination.

On Syria, Mr. Kaine said he believed the Obama administration had sent “a mixed message” about whether President Bashar al-Assad had to be deposed after crossing Mr. Obama’s so-called red line forbidding Syria to use chemical weapons. Still, Mr. Kaine said he supported the administration’s decision not to focus on ousting or replacing Mr. Assad and instead to concentrate on battling the Islamic State in Syria and elsewhere.

On CNN’s “State of the Union,” Gov. John Kasich of Ohio, who challenged Mr. Trump for the Republican nomination and has refused to endorse him, ruled out voting for Mrs. Clinton in November, as some Republicans have said they would do. But asked if he would vote for Mr. Trump, Mr. Kasich said, “I wish that I could be fully enthusiastic — I can’t be — so I don’t know what’s going to happen in the end.”