The double world champion, who did 119 laps of Barcelona's Circuit de Catalunya compared to just six on a troublesome first day in Jerez last year, faced questions about his commitment to the Honda-powered team after a nightmare 2015.
With one British bookmaker reportedly offering odds of 3-1 on the Spaniard not seeing out the season, the driver moved to reassure fans that he had no intention of walking away.
"I need to check that website," he smiled.
Asked how much he would be prepared to bet, he replied: "Everything. All week has been some rumours...when there are too many weeks or months with no track action there is a dangerous tendency to be creative on the news.
"We are on track and hopefully no more rumours," he said. Asked again whether he would see the season out, Alonso replied: "Of course. And the next one."
Speaking later to Spanish reporters, the former Ferrari driver reiterated: "I have a contract for three years. I'm not thinking about anything else. This is a very important year for us."
Alonso crashed at the circuit on Feb. 22 last year, ending up in hospital with concussion and missing the opening Australian Grand Prix.
The crash was just one low in McLaren's worst ever season, the start of a new partnership with Honda turning into a sequence of engine failures and frustration at the lack of performance.
In comparison, Tuesday offered a far more optimistic outlook even if the programme was all about basic aerodynamic study and reliability tests rather than any attempt to probe the car's ultimate performance.
Alonso said the engine had definitely improved, but that had never been in doubt given just how much performance was lacking last year. He said he was proud of what the team had done and his motivation was high.
"I think on the aerodynamic side there are some parts that are quite innovative and new, in our car at least," added Alonso. "The others had these ideas in the past but for us they are new.
"We need a little bit of time to mature the package and in the power unit the same thing. For us last year was a lot of learning, a lot of pain, but we learned many things."
The season starts in Australia on March 20.
(Reporting by Alan Baldwin, editing by Toby Davis)
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