Cameron named the mayor of London and potential leadership contender Boris Johnson, known for his bumbling image and mop-top hairstyle, to a senior political role but not a ministerial position.
"As promised, he will devote his attention to his final year as mayor of London," Cameron said.
Many ministers from the previous government held on to their jobs including finance minister George Osborne, another potential leader who was promoted to a post as Cameron's number two in government.
Read: Cameron shapes new team after stunning UK election win
Theresa May has been re-appointed as home secretary and several women were promoted to more junior positions, after Cameron promised that a third of his Cabinet would be made up of women.
Cameron also held talks with Conservative backbenchers amid concern that right-wingers in his party could play a disruptive role for the government, particularly over Britain's EU membership.
The British leader was expected to tell the influential 1922 Committee of backbenchers that his new five-year term would be about renewal, compared to a first term focused on "repair and recovery" to get the country out of a painful recession.
"It will be our task to renew a sense of fairness in our society - where those who work hard and do the right thing are able to get on," Cameron was expected to tell the MPs, British newspapers reported.
Read: The UK general election
The Conservatives won 331 out of the 650 seats in the House of Commons in Thursday's election, which gave Labour 232, the pro-independence Scottish National Party 56 and the Liberal Democrats just eight.
With the exception of nationalists in Scotland, the election left Britain's opposition in disarray, following Friday's resignations of Labour leader Ed Miliband and Liberal Democrat chief Nick Clegg.
The Labour party is split between centrists and leftists and was due to hold initial talks on Monday on finding a new leader ahead of a formal meeting on Wednesday of its national executive committee.
The SNP lawmakers meanwhile arrived for their first day in Parliament accompanied by the party's leader Nicola Sturgeon, who has called for sweeping new autonomous powers for Scotland that would go much further than any past promises of devolution.
Sturgeon, who as Scotland's first minister did not stand for Parliament herself, has said that after SNP gains "it simply cannot be and it will not be business as usual when it comes to Westminster's dealing with Scotland".
MPs will be formally sworn in next Monday and Queen Elizabeth II will deliver her traditional speech at the State Opening of Parliament on May 27, which will outline the Conservatives' legislative proposals.
Cameron has promised to hold an EU membership referendum by the end of 2017 and to eliminate Britain's budget deficit of some £90 billion (125 billion euros, $139 billion) by 2018-2019.
Anti-austerity campaigners clashed with police outside Downing Street on Saturday and are preparing a larger demonstration next month against impending severe budget cuts to bring down the deficit.
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