It is "unacceptable" for women to find their male colleagues have been paid more in bonuses, Nicky Morgan has said.
The Government has announced firms will be forced to include bonus payments when they publish details of the pay gap between men and women employees.
The Education Secretary and Minister for Women and Equalities said having unequal pay for the same job was outlawed 40 years ago, but there was still a 19% gap between the average of men's pay and women's pay.
She told BBC Radio 5 Live's Pienaar's Politics: "Today we're saying we've been consulting on regulations to make companies with over 250 employees publish information about the average pay of male employees and female employees, we now want them to go further by including information about bonuses paid to male and female employees, we also want to extend that duty to the public sector, including I might add the BBC."
Asked if there was a suspicion that bonuses were paid in a "cronyist sort of way", she added: "Possibly, absoIutely, I think if you read any of the articles on this, you'll often find that actually when women ask the question about bonuses, they'll find that their male colleagues have been paid more in bonuses than they have, we think that is unacceptable."
She said the Prime Minister had been "very clear" that "we want to eliminate the gender pay gap in a generation".
Ms Morgan said reporting of such information "does concentrate minds".
She told BBC One's The Andrew Marr Show: "In terms of the reporting, I think it does concentrate minds when companies see the gender pay in their own company of their employees including bonuses. I think that does then change, start to change behaviours, it has the conversations in the company."
Ms Morgan said the Government also wanted to see women on all boards of FTSE 350 companies - after a target of getting women into at least a quarter of boardroom seats in FTSE 100 firms was met.
Lord Davies - who set that target as part of a government-commissioned review - is due to outline final recommendations.
She added: "Well this is about executive boards what we've seen, and I'd like to thank Lord Davies for his work because actually we've now got over 25% of all positions in FTSE 100 companies are held by women, but you're right obviously that, we've particularly made progress with non execs, it is now about execs, but it's also about building a pipeline.
"The thing about the gender pay gap is understanding why does it happen, often it's women aren't in high enough pay and careers, they don't get to stay in longer before they take time out, it's all those things, it's building that pipeline of talent."
Asked about the prospect of her running for party leader or prime minister, she said her three jobs were keeping her "pretty busy", but added: "Look I've been a member of the party for 26 years, it would be an extraordinary honour to be even considered to be leader."
She said it would be "great to have a woman in the leadership running when the time comes".
Parliament, she added, needed to be more diverse but she was not in favour of having specific quotas for female MPs.