Mallya said Force India would not be following Marussia and Caterham onto the sporting scrapheap.
The Briton leads Rosberg by 24 points with two races, and a maximum 75 points, remaining.
Button has said previously that he wanted to stay at McLaren, who have been closely linked to Ferrari’s Fernando Alonso.
Hamilton has pledged to work as hard as possible to triumph again in his bid for a second championship.
After a successful US Grand Prix, championship all but in Briton’s hands as win takes him 24 points clear at the top.
Briton stretched his lead over team mate Rosberg to 24 points with two races and a maximum of 75 points remaining.
F1 faces a crisis that may signal the end of the Ecclestone era and F1 in its modern image.
The India-born Sauber principal said the predicament of Marussia and Caterham showed the need for cost-cutting measures.
The 29-year-old has a 17-point lead over his rival Nico Rosberg, with three races still remaining.
A team spokesman said on Wednesday that the 43-year-old had tendered his resignation way back in March.
Lewis Hamilton continued his good run despite being driving on the brand new circuit of Sochi.
FIA on Saturday said that each and every life is important and they can’t afford to put them in jeopardy.
In 2012, tests were carried out using a forward roll hoop after other experiments with a jet fighter-style canopy.
Formula One supremo Bernie Ecclestone has shrugged off the critics and President Vladimir Putin.
Bianchi aquaplaned off the wet track with his car hitting the rear of a tractor deployed to remove Sutil’s car.
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