Asked in the Suzuka paddock whether the frustrated world champions would be staying, Dennis replied: "Yes, what more do you want?".
"Jenson has a two-year contract," he told reporters, adding that it would remain unchanged and Button, who has hinted he could retire at the end of the season, was happy with the arrangement.
"I should have taken away any doubt about our commitment to him earlier than I did," continued Dennis, who said he told the 2009 champion on Thursday.
"It would have been more constructive if he had known I had no intention to exercise our option to terminate. We did not put it in there to exercise it and we didn't... I informed Jenson accordingly."
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Alonso, who assured reporters on Saturday he would be at the Honda-powered team next year, said after the race that he did not know.
Dennis told reporters he too did not know what the Spaniard was talking about: "I spoke to him earlier today. He has got a contract. He understands the contract. I am surprised at the comment," he said.
In a very public humiliation for Honda at their home circuit, and with the car giant's top bosses attending, Alonso had vented all his frustration with the underperforming engine as he laboured to 11th place -- an impressive result in the circumstances.
"I'm being passed down the straights like a GP2 (car). This is embarrassing, very embarrassing," the double champion said over the team radio, referring to Formula One's less powerful feeder series.
Later, after being passed by Max Verstappen's Toro Rosso, he repeated "GP2 engine, GP2."
Dennis, whose once dominant team are ninth out of 10 in the standings and enduring their worst season with just 17 points, said he understood the Spaniard's frustration but could not condone the outburst.
"It does not show the professionalism that I would like all of our drivers to show," he said.
"Am I going to go ballistic? No. I will handle it in my own way and my way is not in public."
Button, who finished 16th, had described trying to fend off other cars during the race as being like a "Samurai without his shield or sword".
(Editing by Sudipto Ganguly)
