Unions met with Kretinsky’s EP Group over the weekend to hammer out the additional commitments and have agreed the package in principle but need to put it through “the internal democratic process”.
Royal Mail, which was split from the Post Office and privatised a decade ago, has seen its performance deteriorate in recent years, leading to heavy financial losses.
Customers have also complained about deliveries, with important medical appointments and legal documents not delivered on time.
Last week, Royal Mail was fined £10.5m by the regulator Ofcom for failing to meet delivery targets for first and second class mail.
Ofcom said Royal Mail’s poor service was “now eroding public trust in one of the UK’s oldest institutions”.
Royal Mail owner International Distribution Services (IDS) said externally it had carried out “substantial” reforms this year to try to drive improvements.
The volume of letters being posted in the UK has plummeted, with half the number being sent compared to 2011 levels.
Meanwhile, parcel deliveries have become more popular – and more profitable.
Parent company IDS made a small profit last year which was entirely generated by its German and Canadian logistics and parcels business, off-setting losses at Royal Mail.
Mr Kretsinky told the BBC he intends to invest heavily in the roll out of delivery lockers to make online deliveries more efficient as has happened across Europe.
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