The party won seven seats in last week's election and those MPs travelled to London on Tuesday to claim their offices.
With a fall from 331 to 318 seats in the House of Commons, May is first tapping the socially conservative Democratic Unionists (DUP) of Northern Ireland (DUP), winners of 10 seats, for an arrangement to keep her minority government in power. Ms May is due to meet its leader Arlene Foster on Tuesday. But depending on what kind of deal takes shape, the vocal opponents of the European Union among the Conservative Party and general public who had hoped to end policies such as freedom of movement may end up severely disappointed.
Scotland's Conservatives finished with 13 seats, their highest seat total in an United Kingdom election since 1983, and with their highest popular vote share since 1979.
She also indicated that there will not be a second general election this year.
Ruth Davidson, the leader of the Scottish Conservatives, leaves a cabinet meeting at Downing Street in London.
May's failure to get a majority has undercut her tough Brexit strategy, which had raised fears that Britain was heading for a so-called "hard Brexit", which could potentially see tariffs slapped on British exports to the bloc.
Sinn Fein MPs have traditionally refused to sit in Westminster because they won't swear an oath to the Queen.
The first move in Mrs May's new reality of compromise politics is to listen to what the DUP hope to gain by offering the Conservatives their support. Neighbouring Ireland's Prime Minister, Mr Enda Kenny, publicly voiced his country's "concerns" at this danger.
There are also the considerations closer to home.
Some observers have maintained that a deal with the DUP risks destabilising Northern Ireland by increasing the influence of pro-British unionists.
The Remain side in Northern Ireland won with almost 56 per cent of the tally although there was disparity geographically, with the south and west being much more opposed to Brexit.
Ireland's violent recent history from the 1970s and 1990s is also a factor, at least symbolically.
Ruth Davidson dismisses Scottish Tories breakaway claim
Nevertheless, independence was not the only reason why the SNP suffered its first significant electoral setback in a decade. Certainly, this general election makes the prospect of an independence referendum in the near future far less likely.
She added she hoped people on mainland Britain would "find out a bit more about Northern Ireland and understand it a little better" once a deal with the DUP is struck.
The Northern Irish party's stance on equality has been under scrutiny this week, as numerous MPs that Theresa May will be relying on harbour actively homophobic views.
The British government is preparing to share power with a Northern Irish party, that is known, if at all, for its anti-gay views and for its links with sectarian killers.
His appointment as Environment Secretary came after former chancellor George Osborne branded her a "dead woman walking", warning that she could be ousted from No 10 in a matter of days.
Amid rumours that he is plotting a leadership challenge against May, Foreign Secretary Boris Johnson has stressed his support for the prime minister.
Labour Leader Julia Gillard in Australia was able to forge a working relationship with MPs from other parties in 2010.
On Monday, she faced members of the Conservatives' 1922 Committee, which can trigger a vote of confidence in a party leader if it receives letters from 15 percent of the party's MPs.
In contrast to the Australian situation, where the economic forecast was positive, the United Kingdom is awash in uncertainty after two general elections, a leadership change and the vote to leave the European Union in the past two years.
"The reason for leaving the single market is because we want to take back control of our borders, they're not compatible", he told BBC Radio.
May has stayed on the tightrope so far by firing two key advisers and reshuffling her cabinet to keep all factions of the party on board.
May also restored former Justice Secretary Michael Gove to the Cabinet in another move created to show she was willing to listen to critics.
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