The 68-year-old had been in charge for four years after replacing Italian Fabio Capello but has won just three of 11 games in major tournament finals.

Iceland - with a population of just 330,000 - were among the lowest-ranked teams in France at 34 in the world.

"I'm sorry it will have to end this way but these things happen," Hodgson said.

"I hope you will still be able to see an England team in a final of a major tournament soon.

"Now is the time for someone else to oversee the progress of a hungry and extremely talented group of players. They have done fantastically, and done everything asked of them."

Hodgson, who won 33 of his 56 games in charge, would have been out of contract at the end of the tournament and was set to have talks over having it renewed.

FA chairman Greg Dyke had stated he would only stay on if England "do well" in France, indicating that meant at least reaching the quarter-finals - but they needed to beat Iceland to do that.

In a statement issued following Hodgson's resignation, the FA said: "Like the nation, we are disappointed to lose this evening and that our run in Euro 2016 has come to a premature end.

"We had high hopes of progressing through to the latter stages of the competition and accept that we have not met our own expectations or those of the country.

"We back Roy Hodgson's decision to step down as England manager and will discuss next steps imminently."

England qualified for Euro 2016 with a 100% record in their group. They started the finals with a 1-1 draw against Russia before beating Wales 2-1 and drawing 0-0 with Slovakia in their final Group B game - results that left them in second place and in a tougher half of the draw.

Hodgson faced heavy criticism following the Slovakia game for making six changes to the side that had beaten Wales.

Under Hodgson's guidance, England had reached the quarter-finals of the last European Championship, losing to Italy on penalties, before a dismal showing at the 2014 World Cup where they went out at the group stages without winning a game.

Speaking to reporters following Monday's last-16 defeat in Nice, Hodgson confirmed his assistants Ray Lewington and Gary Neville would also be leaving their posts.

BBC Match of the Day pundit and former England international Alan Shearer - who revealed he went for the England job before Hodgson was appointed - said of the Iceland defeat: "That was the worst performance I've ever seen from an England team. Ever. We were outfought, outthought, outbattled and totally hopeless for 90 minutes.

"It looked to me like Roy was making it up as he was going along. Tactically inept. We had players in the squad who didn't deserve to be there. Harry Kane on corners, the list is endless.

"Our players caved tonight. We've all played under pressure - they caved and the manager caved."

Fellow BBC pundit Jermaine Jenas added: "The one thing that stood out is that I don't think Roy knew what he was doing. He didn't know his best team or system. His loyalty to players has cost him his job. It was a horrible way to go out of the tournament."

But England goalkeeper Joe Hart said: "The next manager has a tough job on his hands. We worked hard but with no success. That is how this team will be remembered."

England captain Wayne Rooney added: "It's a sad day for us. It's tough. There are always upsets in football. It's not tactics. It's just unfortunate. We know we're a good team. I can't stand here and say exactly why it's happened.

"Roy Hodgson will look back and think what he could have done differently.

"I'm still available to play. It'll be interesting to see who comes in."

(BBC)