The Royal Mail is offering a £300 bonus to any of its 150,000 staff who cross the picket line in any forthcoming nationwide postal strikes.

Moya Greene, its chief executive, wrote to all employees before Wednesday's strike ballot result to offer the sum if they continue working while colleagues are out on strike.

The offer came as MPs said they would call the business secretary, Vince Cable, back to parliament to answer claims that he "massively shortchanged taxpayers" by pricing the shares in the Royal Mail too low. Lazard, the investment bank that collected millions of pounds from the government for its advice on how to price the shares, will also be called to give evidence before the business select committee.

Royal Mail's shares rose to 489p on Tuesday – 48% more than the government sold them for on Friday. If the government had sold the shares at 450p, rather than 330p, it would have made an extra £600m for the taxpayer on top of the £1.7bn it made from selling the 52% stake in Royal Mail.

Greene's last-ditch attempt to avert the first nationwide strike in four years came as the Communication Workers Union (CWU) said it was confident workers would back industrial action when it announces the results of a strike ballot on Wednesday afternoon.

Postal workers described her offer as an "act of desperation and discrimination" and a "scab bonus". Paul Firmage, one of the 371 of Royal Mail's 150,000 staff to rejected free shares in the privatisation, said the £300 bonus was "yet another bribe".

"They are offering people money to be a scab. It is a scab bonus," he said."

The CWU said: "It's an act of desperation and discrimination. We believe it's irrelevant and will make no difference to the strike ballot."

In a consultative ballot this year 96% of postal workers were opposed to the privatisation, which they said will erode their pay and conditions.

If staff have voted in favour of industrial action, the first strike could take place on 23 October and would likely be followed by a series of rolling strikes in the runup to Christmas.

In a letter to staff, Greene said: "We offered a lump sum of £300 (pro-rata to part timers), payable in December, as long as there is no industrial action. Many of you have said to me that it is unfair that people should lose this money if others in their office go on strike and they work normally. I agree. So, we would make this payment provided you have not taken action yourself."

Greene, who toured the TV studios on Tuesday to promote Royal Mail's first official day as a private company, also claimed it needed protections from the threat of strike action and that strikes may lead to more job losses. "We need to start thinking about what sort of protections do we need as a company from our people, from what has been probably too quick an approach to resort to industrial action," she said in an interview with ITV News.

On Sky News, Greene warned staff that strikes may put thousands of jobs at risk. She said Royal Mail could only continue to provide high quality jobs with good protections and benefits if the company remained strike-free. "It is a competitive world that we are in, [so] if we ever disappoint our customers... then we put a lot at risk," she said.

Greene, who was paid £1.6m last year, was given £2,200 worth of shares for free, along with all of Royal Mail's staff, and bought a further £10,000 worth. She had tried to buy hundreds of thousands of pounds worth of shares but was scaled back to £10,000 alongside hundreds of thousands of others following overwhelming demand. Her stake was worth £17,568 at Tuesday's closing price.

The 227 shares each bought by 690,000 members of the public were worth £1,110 on Tuesday night – £361 more than they were bought for on Friday.

Peter Hargreaves of the brokers Hargreaves Lansdown said the shares were "absolutely underpriced and the issue badly managed".

Cable, who has dismissed the share price rise as "froth", faced calls to resign over his handling of the privatisation.

Mario Dunn, director of the Save Our Royal Mail campaign, said: "The share price today is proof positive that the government chronically undervalued Royal Mail. This is larceny on a grand scale. Vince Cable has the temerity to call the matter froth.

If Mr Cable thinks ripping the taxpayer off by a billion pounds is froth then he is not fit for office. Mr Cable should do the decent thing and resign."