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8 year oldThe Indiana governor told reporters he is fine after the rough touchdown at LaGuardia Airport. No one was injured.
Mr Pence and the other 30 or so passengers were evacuated through the back of the plane. He was coming from a campaign event in Fort Dodge, Iowa.
LaGuardia Airport has been closed until further notice, said officials.
The pilot slammed on the brakes and passengers on the aircraft could smell burning rubber.
Live TV footage showed Mr Pence standing in the rain near the plane among emergency vehicles, talking to police and other officials.
He tweeted: "So thankful everyone on our plane is safe. Grateful for our first responders & the concern & prayers of so many. Back on the trail tomorrow!"
He said mud had splashed on the front windows of the cockpit.
Republican presidential nominee Donald Trump called Mr Pence to check on him after the incident, the campaign said.
"Mr Trump did reach out to Gov Pence. He's glad that everyone on board is safe," Trump spokeswoman Stephanie Grisham said in an emailed statement.
He was in a motorcade en route to a rally in Geneva, Ohio.
Mr Pence cancelled a fundraising event that he was to take part in at Trump Tower in Manhattan, and headed to his hotel.
It hasn't been a good week for the Indiana governor.
On Wednesday, he announced on Twitter that his dog, a beagle named Maverick, had passed away aged 13.
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