A triumphant Jeremy Corbyn has pledged to reward Labour’s mass membership with more power over the running of the party, after he inflicted a thumping defeat on leadership challenger Owen Smith.

Corbyn, who secured almost 62% of the vote – an even bigger mandate than a year ago – told the Observer that his victory was a personal “vindication” that had increased his power and authority to create a mass democratic movement from the grassroots upwards. Smith secured 38% of the 506,438 votes cast.

Setting out his plans for phase two of his leadership after a year of bitter disputes with his MPs, Corbyn said: “I have been given the authority by the members and that is what I intend to deliver on.”

While he insisted he would now “wipe the slate clean” and offer a way back for rebel MPs who had plotted to remove him over the summer, he made clear that it was ordinary members – his power base in the party – who now had to be given a greater say in a remodelled Labour party.

“The participation is even higher, and my majority is bigger, and the mandate is very strong. So let’s use it to reach out,” he said. “With this huge membership, that has to be reflected much more in decision-making in the party.”

Meanwhile, his shadow chancellor, John McDonnell, said that, in a year’s time, the membership could reach one million.

Corbyn made it clear that with a current total of well over 600,000 members, the grassroots needed far greater representation on key bodies, such as the national executive committee (NEC).

“I recognise that to be successful, the party has to reach out to all sections and I will do that,” he said. But he added that MPs and others had to understand “that we have this enormous party membership … they are the people that raise the money, knock on doors, deliver the leaflets, do the campaigning work”.

Shadow chancellor John McDonnell says the party’s membership could reach 1 million in a year’s time. Photograph: Peter Nicholls/Reuters

Any hope that this second decisive Corbyn victory in a year would tempt senior figures who quit the shadow cabinet over the summer back into the fold were quickly dashed as several said they would return only if the leader allowed MPs to choose most of the members of his shadow cabinet.

Former shadow education secretary Lucy Powell said the party was “more divided than I have ever known” and made it clear that her return to the frontbench would be conditional on Corbyn agreeing that MPs would elect the shadow team.

Corbyn said the issue of shadow cabinet election was open for discussion but refused to commit to the MPs’ demands, saying it was part of a wider debate about how to increase democracy in the party.

A meeting of the NEC failed to come to a resolution on shadow cabinet elections on Saturday evening. Further talks will take place on Monday. It is understood the NEC is likely to organise an “away day” to discuss party democracy.

Smith, the former work and pensions spokesman, warmly congratulated Corbyn, but again ruled out returning to the shadow cabinet. “Jeremy has won the contest,” he said. “He now has to win the country and he will have my support in trying to do so.”

After a three-month contest which was at times bitter, Corbyn won clear majorities in all membership categories – full members, registered supporters and affiliated members. Smith’s supporters said their man polled the most votes among those who had been members before 2015.

The result left critics of Corbyn and people on the right of the party searching for a way forward after the attempted summer coup against the leader backfired spectacularly. Leading figures on the so-called Blairite wing of the party, including Chuka Umunna and Tom Baldwin (who was Ed Miliband’s press secretary), meanwhile, have laid out their ideas in the Observer for keeping the moderate flame alive.

Alison McGovern, chair of the Blairite thinktank Progress, said that Labour needed a new vision, as well as a new leader. “A change of leader is necessary, but not sufficient, for Labour to find its voice again. Britain isn’t waiting for Labour to catch up; it’s us who need to catch up with Britain.”

McDonnell, Corbyn’s close friend and ally, has told the Observer that it is now up to members of the leadership to show they would listen to the concerns of all those in the parliamentary party, and aim to learn lessons from them. He insists there is no plan for a “purge” of party officials, including the general secretary, Iain McNicol, who crossed swords with Corbyn during the leadership contest. “We are happy for him to remain, simple as that,” he said.

McDonnell says many of those who resigned over the summer have approached the leader’s office to express interest in returning. “There have been some discussions with [former] shadow cabinet people, and a few on the second and third tiers, and that is great.”

The party now has to prepare for a possible general election as early as next May and is already looking at appointing an advertising agency to help run the campaign. “I think that if Theresa May is going to go [for an early election], it will be May or October,” he says. “But we have got to be prepared whenever it is.”

The shadow chancellor says the party now has more money in its coffers than at any time in the past 20 years and is ready to take on the Tories. He stresses that a membership that could reach a million had to be fully involved and offered opportunities to participate.

“We could be in a situation by next year where we have got a million members. We have to got to come to terms with how you organise that and how you make sure they can fully participate.”

Corbyn called on MPs to join a campaign day next weekend against the Tories’ plans to reintroduce grammar schools, to show that the entire party can now unite.