Russia was suspended by governing body the IAAF for state-sponsored doping in November 2015, a ban extended on Monday to cover the 2017 World Championships.
Mutko, who was criticised by the IAAF on Monday, accepted "there were many abuses and breaches" but says "colossal work has been done" over the last year.
Russia expects to be back by November.
A return to competition will require the reinstatement of the national drug-testing agency, which remains suspended over various allegations of covering up doping.
Mutko - who assumed his role in October - has been outspoken since the McLaren report alleged there had been a state-backed Russian doping programme. In January he said female doping results can be distorted if athletes have had sex in the days leading up to a test.
But on Monday he said: "Athletes broke the rules and many coaches don't understand how to work without doping and it's high time for them to retire."
Russia will miss the World Championships which begin on 4 August in London, but some athletes from the country could compete in London under a neutral banner.
The IAAF is so far considering 35 applications from athletes, who could be included if they can show a record of independent drug-testing by agencies other than the suspended national body.
Russian track federation vice president Andrei Silnov said he was against the inclusion of neutral athletes in principle but also questioned if the country's problems were as bad as the IAAF outlined.
"It's all being solved, slowly but surely. We're doing what we need to do," Silnov said. `"They say we have a culture of doping. What culture of doping?"

The 40-year-old former New Zealand player is currently forwards coach at Clermont Auvergne and he previously held a similar position at Leinster.
Gibbes will work under director of rugby Les Kiss, while current head coach Neil Doak's future is unclear.
"The respect I have for Les as a coach and person was one of my main reasons for making this decision," said Gibbs.
Ulster are sixth in the Pro12 table and out of the European Champions Cup in what has been a largely disappointing season.
"Les sold his vision of where he wants to take Ulster over the next few years," added Gibbes.
"Ulster is a team that I know well, having come up against them on a number of occasions. The Clermont-Ulster games this season gave me an insight into the strengths of the squad and it's exciting to think that I'll be part of that environment from next season."
Gibbes, who joined Leinster in 2008 and won three Heineken Cups during his spell in Dublin, said: "With six years at Leinster and three at Clermont in the Top 14, I've been afforded many different experiences, working with some very talented coaches and players.
"I hope to apply what I've learned to the role at Ulster and my family and I are looking forward to integrating into a strong community in Belfast."
He moved to France in 2014 and was part of a coaching set-up that guided Clermont to the Top 14 and Champions Cup finals in his debut season.
"Jono's CV speaks for itself and I know that he's looking forward to joining Ulster and working with the team," said Kiss, 52.
"Since his retirement from playing, Jono has had an integral role in the coaching teams of two of European rugby's most successful sides.
"Jono's expertise as a forwards coach is obvious, however his wealth of knowledge in other areas of the game will be really important for us."
"A review of the coaching structure is ongoing ahead of next season and the appointment of Jono as head coach is the first part of that process.
"A further announcement will be made in the coming weeks, which will focus on getting the right balance in our coaching team."
Russian coaches who "do not understand how to work without doping" should "retire" says the country's deputy Prime Minister Vitaly Mutko.
[NEXT_CONCEPT]
Jono Gibbes is to become the head coach of Pro12 side Ulster on a two-year deal in the summer.