The Immigration Minister Damian Green has said the low turnout in the strike ballot, which saw just one in five vote, showed most union members did not back a walkout.
He told the BBC's Newsnight: "PCS members don't want this strike to happen; seven out of eight of them didn't vote for a strike.
"They are patriotic people, they care about their job, they care about the reputation of this country.
"It's a small group in the union leadership that is behaving disgracefully, trying to make political capital out of the Olympics, which is meant to be a great national celebration."
He said previous action failed to cause significant disruption at Heathrow, with enough staff available to replace strikers.