Mrs May announced on Friday she would seek to form a minority government with the help of a small Northern Irish party, the ultra-conservative Democratic Unionist party (DUP).
May's Conservatives unexpectedly lost their majority in parliament in snap vote, causing political chaos ahead of Brexit talks with EU.
Brexit Secretary David Davis said that some policies planned before the election would be pruned back.
Britain's chief negotiator for leaving the European Union says the talks for exiting the trading bloc may not start as scheduled next week.
Senior figures, including Foreign Secretary Boris Johnson who is touted as the favorite to replace May should she be forced out, have pledged loyalty and called on colleagues to rally behind her.
"There can be no backsliding from the objectives the PM set out in the [election] campaign - taking back control of our laws, our borders, our cash; but also ensuring that we have a great new partnership with the European Union that allows us to trade more freely and enthusiastically than ever", Mr Johnson wrote in the right-wing tabloid The Sun.
After Mrs May addressed the 1922 Committee of backbench Tory MPs on Monday, some of those present suggested the PM would consult more with business on her approach to the talks.
The change of position comes after Prime Minister Theresa May lost her majority in the House of Commons in a disastrous election last week.
A contrite May took responsibility for losing her party's majority; 'I've got us into the mess and I will get us out of it.' She also promised to help those who had lost their seats and said sorry a few times.
Germany: number of Britons granted citizenship quadruples
On average, only 1.6 per cent of all applications for German citizenship that are granted come from European Union countries. The second largest national group, Poles, recorded an increase of 11.3 percent to reach 6632 naturalizations.
In the hours immediately after Thursday's embarrassing election setback for the Conservatives, British media reported that finance minister Philip Hammond had told May she needed to put "jobs first" in any new deal with Brussels.
Thursday's calamitous result has also left May hugely weakened within her own party, and the Prime Minister has already signalled a move towards conciliation with pro-European MPs. If she fails to convince them, calls are likely to mount for her to step aside, and a leadership contest could be triggered if 15 percent of MPs write to the head of the 1922 Committee saying they have no confidence in her.
The Federation is pushing for the United Kingdom to remain in the single market and customs union, and is against restrictions on free movement.
May will meet DUP leader Arlene Foster in London on Tuesday but will face demands from the DUP for more money for Northern Ireland. Setting the tone, Michael Heseltine, a leading pro-European Conservative told the BBC's Andrew Marr Show on Sunday that "hard Brexit" was "the cancer gnawing at the heart of the Conservative Party".
He told the Today Programme: "What we've said is that we need those benefits, and whether they're achieved through reformed membership of the the single market and the customs union, or through a new, bespoke trading arrangement, is actually secondary to achieving the benefits".
As discussion continued, a leading business organization said the political uncertainty is leading to a "dramatic drop" in confidence.
On Monday, the currency was under pressure once again.
"The UK has had a reputation, earned over generations, for stability and predictability in its government", said a senior executive at a multi-national company listed on the London FTSE 100, speaking on condition of anonymity. President Macron is on course to win a huge victory after the first round of parliamentary elections. "That has really profound implications for multinational businesses that have made a long-term bet on London being the sensible place to base themselves".
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