A senior aide to Mr. Trump said that as part of an agreement to give Mr. Cruz a prominent speaking slot, Mr. Cruz would not disrupt the proceedings of the nomination and the campaign would be able to review the speech before it is delivered.

Some senators who attended the meeting said that it was largely cordial and thoughtful and played down Mr. Trump’s occasionally gruff tone.

“He didn’t defeat 16 opponents by parroting Republican establishment talking points,” said Senator Jeff Sessions of Alabama, one of Mr. Trump’s most stalwart supporters.