Donald J. Trump’s unabashed and continuing hostility toward the parents of a slain Muslim American soldier, and his attacks on Republican leaders who have rebuked him for it, threaten to shatter his uneasy alliance with the Republican Party at the outset of the general election campaign.

Ignoring the pleas of his advisers and entreaties from party leaders in Washington, Mr. Trump only dug in further on Tuesday. He told a Virginia television station that he had no regrets about his clash with Khizr and Ghazala Khan, the parents of an Army captain killed in Iraq. And in an extraordinarily provocative interview with The Washington Post, Mr. Trump declined to endorse for re-election several Republicans who had criticized him, including the House speaker, Paul D. Ryan of Wisconsin, and Senator John McCain of Arizona, who both face primaries this month.

He also belittled Senator Kelly Ayotte of New Hampshire, who had criticized his treatment of the Khans, for not being supportive of his campaign.