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.
Home Office job adverts would appear to show that unions 'won' the dispute, but Damian Green denies there are any new jobs.
The Public and Commercial Services Union (PCS) has cancelled plans to strike tomorrow - the day before the Olympic Opening Ceremony.
The Government is considering court action to prevent a planned strike by Border Agency staff on the eve of the Olympics.