Cameron's decision to resign expected to set off an intense Conservative Party leadership battle.
Among the likely contenders are former London Mayor Boris Johnson and Justice Secretary Michael Gove, who both helped lead the "leave" campaign.
Other Cabinet members are likely to contend as well.
Defense Secretary Michael Fallon said it is too early to speculate about who will replace Cameron.
"I think it is a bit too early to start speculating about that," he said. "There is plenty to do now to help make this decision work, to stabilize our economy, to reassure our allies and to continue the program we were all elected on last year."
He said Cameron has done the honorable thing by resigning.
Cameron had been expected to serve several more years. He was re-elected last year with a majority vote but lost control of the European Union debate.
With his wife Samantha at his side, he said he is not the correct "captain" to steer Britain through its upcoming negotiations.
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