The OPEN RANGE star, 49, was "initially hurt" when he saw Madonna's furious reaction to Costner telling her he enjoyed her "neat" show, when he visited the superstar backstage.
But the showbiz feud came to an end when Costner decided to take his daughter along to one of Madonna's concerts.
Costner explains, "A lot of people thought it was strange that I'd want to go to her concert. But my daughter LILY is a singer and I didn't want to keep my kids from seeing Madonna because I had my feelings hurt, or I was semi-embarrassed or whatever.
"We were sitting in the audience and Madonna dedicated a song to me. I thought it was very classy."
The OSCAR-winner has never thanked the MATERIAL GIRL for her offering, but regards it as concluding their dispute.
He continues, "I've never talked to her about it or written her a thank you note. I thought it very brave on her part and I respected it.
"What was really cool was that my kids heard that dedication from Madonna. They knew we were going to see someone that in one moment in time, there was some difficulty between us. Madonna didn't make a big deal about it but it was a big deal to me and I appreciate it.
"I like her and I think she is an important person in our entertainment history. Maybe some day we will chat together."27/02/2004 19:20