Alonso missed today's race – the most prestigious in the Formula One calendar – to compete in the Indy500.
That prompted McLaren to bring in Button – five months after he announced his retirement.
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Button was 12th fastest on his one-off return only to be hit by a 15-place grid penalty, forcing him to start from the pitlane.
As Button pulled in to position before the race, Alonso came on the driver's radio to wish the Brit luck.
Jenson Button joked with Fernardo Alonso ahead of the Monaco Grand Prix F1 Monaco Grand Prix: Stars spotted in the pit lane Sun, May 28, 2017
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I am going to pee in your seat
Jenson Button to Fernando Alonso
Speaking from Indianapolis, Alonso said: "I am sure you don't want to hear my voice before you start but I just want to say good luck and I will be watching you here."
Button laughed and said: "Aww thanks mate. I am going to pee in your seat!"
Alonso replied: "Please don't do that!”
Button, who won the world title in 2009, spent the winter in California training for Ironman triathlons.
He signed a contract with McLaren last autumn committing him to replacing any race driver not able to take part in a Grand Prix this year.