Ministers have discussed introducing Ronald Reagan-style employment laws which would allow them to sack UK Border Agency staff who plan to strike the day before the start of the Olympics, the culture, media and sport secretary said on Sunday.

Jeremy Hunt said that the option had not been ruled out as thousands of staff at the Home Office, including the UKBA workers, prepare for a 24-hour strike on Thursday in a row over jobs, pay and other issues. He was responding to a question from BBC presenter Garry Richardson, who himself sparked anger by appearing to ask the minister to dismiss strikers, contrary to impartiality rules. The exchange shows the level of animosity being expressed by ministers and the media towards the Public and Commercial Services union (PCS), the union behind the dispute. It follows reports at the weekend of a plan being developed by George Osborne to introduce new laws which would make it more difficult to go on strike.

Hunt told Richardson on Radio 5 Live's Sportsweek: "Sack them? That is the Ronald Reagan approach," in a reference to the former US president's decision to dismiss more than 11,000 air traffic controllers for being a peril to national safety.

"I can tell you amongst ministers there have been people asking whether we should be doing that, but I don't want to escalate things by talking about that right now, because I know amongst those 600 people there are lots of people who want to do the right thing and turn up for work," he added. London's mayor, Boris Johnson, is among senior Tory figures urging the government to introduce a new minimum vote threshold for strike ballots. Other proposals, in line with some other EU countries, include setting basic requirements for public services during strikes which would cover transport, hospitals, education and border control.

Richardson, who can also be heard on Radio 4's Today programme, had drawn the comments by asking: "It's great that you have got these contingency plans and you have got these people able to come in and you have trained them up to step in. Why not just let those people go on strike and when they want to come back after they have done all their disruption say 'sorry, your job's not there any more'? Sack them." Earlier, he said of the workers: "They are a disgrace, aren't they?"

Some took to Twitter to voice their disapproval of Richardson's comments. ITV anchor Alastair Stewart tweeted: "Toby Young [the author] makes same point as Gary Richardson on border strikers in Sun but he's opinionated columnist. Richardson's a BBC hack. [#]bigdiff."

The strike will involve staff across the Home Office, including the UK Border Agency, the Identity and Passport Service and Criminal Records Bureau. Union officials said a work to rule and overtime ban could have a big impact on border controls and in passport offices because of the amount of overtime worked. The PCS is in dispute with the Home Office on several issues, including plans to cut 8,500 jobs; threatened compulsory redundancies in the passport office in Newport, south Wales; pay rises capped at 1% following a two-year wage freeze; privatisation of services; and alleged victimisation of union representatives.

Mark Serwotka, the PCS's general secretary, told the Sky News Murnaghan programme he still hoped the stoppage could be avoided and a strike was a "last resort" after the government had refused to engage with grievances. "These are not demands about personal gain, they are about defending important services, the security of the country and ensuring that people still have the chance to work all the year round," he said.

Osborne has been pushing for immediate legislation to impose a minimum turnout – possibly 40% – on strike ballots to protect the economy. However, Liberal Democrat ministers, led by Vince Cable, the business secretary, have warned such a move would prove counter-productive.