UPDATE: Rossi later told Italian media:

"I felt sorry for this situation, it seemed to me like the Blues Brothers scene when John Belushi enters the church and sees the light, perhaps it is due to Marc's meeting with the Pope... I'm sorry, but I can decide what to do. At the end of the day, our personal relationship is not important, it only concerns us. We are two riders, let's race together, the important thing is to be calm and do our job well. Everything else is a waste of time, even just talking about it...

"It's not written anywhere that we should go out to dinner."

Meanwhile, Lorenzo told Movistar TV:

"Both are mistaken. Valentino by not giving his hand, it's a little boy's attitude. And by not taking the opportunity to tell fans not to whistle a rival on the podium. And Marc because this affects him a lot, he has to forget what Rossi does."

Valentino Rossi insisted he has 'no problem' with MotoGP rival Marc Marquez - but then refused to shake the Honda rider's hand.

The sport's biggest stars clashed repeatedly in 2015, leading up to the infamous Sepang encounter.

An uneasy truce then developed during 2016, including a first handshake in Catalunya, but their feud was reignited earlier this year when Rossi fell after contact with Marquez in Argentina.

When asked about a recent interview where Marquez was quoted as saying he would like to make peace with Rossi, the Italian replied:

"I hear this, but I don’t know... It sounds to me a bit strange, because in reality we don’t have any problem between me and Marc.

"So I don’t know why we have to make peace. For me it's okay."

Following those comments, Rossi and Marquez were asked if they would be prepared to shake hands, as in the past.

Marquez: "For me it's nice [to hear Rossi say there is no problem] and of course if it's no problem [for him], for me no problem… "

The Spaniard then offered the handshake, but Rossi kept his arms crossed, smiled and shook his head from side to side.

"It's like this. I mean, what can I say?" a smiling Marquez responded. "Already, second time... No problem, I will race the same."

Rossi, also smiling, then spoke: "We don’t need to shake the hand. We are okay. We don’t have any problem."

The exchange is sure to add some extra spice and motivation for both riders at this weekend's Misano MotoGP, held at Rossi's local track.

Asked how it feels to race at a circuit where the crowd are so heavily supporting Rossi, Marquez replied:

"I'm just feeling that I'm leading the championship and riding really well. I feel in a sweet moment."

Ducati rider Lorenzo quipped: "If I was looking in the grandstands, I would not be a MotoGP rider! I'm just looking at the next corner. So it's okay."

Rossi has won seven MotoGP titles, with Marquez on course to win a fifth premier-class crown this season.

The pair are currently first and second in the world championship, albeit with Marquez 59-points clear of Rossi, who is yet to win a race this year.

Lorenzo, who will join Marquez at Repsol Honda next year, is the next most successful on the current grid with three MotoGP titles.