For the first time since becoming head of the Roman Catholic Church, Pope Francis has publicly showed signs of irritation on his trip to Mexico.

Following a colourful encounter with young dancers and singers in the western city of Morelia, Mexico Francis went over to greet the faithful on Tuesday.

Some overly eager people tugged on his sleeve from behind a barrier and appeared to be on the verge of pulling him to the ground.

After it happened a second time, the pope got a cross look on his face and said, "Don't be selfish, don't be selfish."

Francis took a couple of steps back as appeals came over the public address system asking the crowd not to clump together.

The pontiff continued to wave to people a few minutes more before leaving.

During his appearance, Pope Francis urged Mexico's youth to resist the lure of easy money from drug dealers and to instead build up their communities by valuing themselves as the wealth of the country.

Francis sought to offer a message of hope and encouragement to the next generation during a youth pep rally Tuesday in the state of Michoacan, which is a hotspot in Mexico's drug trade.

Francis said he understood it was difficult to feel one's worth when, in his words, "you are continually exposed to the loss of friends or relatives at the hands of the drug trade, of drugs themselves, of criminal organizations that sow terror."

But, he insisted, "You are the wealth of Mexico."

The pope also urged Mexico's priests not to resign themselves to a country dominated by drug-fueled violence and corruption, but rather to be inspired to get out of their comfortable lives and fight injustice.