Boris Johnson has promised tax cuts for businesses and families after narrowly clinging on to power last night.
Conservative MPs have voted in favour of Mr Johnson remaining as their leader by 211 to 148 in the party poll on Monday.
The vote followed a day of drama at Westminster after rebel MPs triggered a vote of confidence in the Prime Minister.
In an effort to win round opponents, Mr Johnson wrote to his parliamentarians to address complaints that he was going against the party’s low tax, small government traditions.
“We will cut the costs of governments. We will cut the costs of business. And we will cut the costs of families up and down the country," he said.
“And we will of course devote all our energy to reducing the biggest single household outgoing of all - the tax bill.
“It must come down, and it will, because that is the best way to deliver the growth we need.”
Mr Johnson said he and Chancellor Rishi Sunak would unveil the measures over the next few weeks.
Four out of Scotland's six Tory MPs voted against the prime minister in yesterday's dramatic vote.
Shortly after the result, Alister Jack said it was time to "put this behind us".
Mr Jack, the MP for Dumfries and Galloway, said: "As I have been clear throughout, the prime minister has my full support. I voted for him tonight, and I am very pleased that he has received the backing of a clear majority of the parliamentary party.
"We now need to put this behind us, and get on with what really matters - tackling the very real major challenges we face both at home and abroad."
Banff & Buchan MP David Duguid was the other Scottish Conservative MP to back Mr Johnson.
“Nothing that’s happened in the last 24 hours has changed my opinion on whether or not the prime minister needs to resign, so tonight I voted against the motion of no confidence,” he said after the vote.
Andrew Bowie, MP for West Aberdeenshire and Kincardine, said he voted against Mr Johnson after listening to the concerns of his constituents.
Scottish Conservative leader Douglas Ross voted to oust the PM, completing a double U-turn on the issue, having originally called for him to go after the 'partygate' scandal, before saying he should remain in post following the outbreak of war in Ukraine.
"Having listened closely to people in Moray who re-elected me to represent them, and from many people across Scotland, now that this confidence vote is upon us, I cannot in good faith support Boris Johnson," he said.
The SNP said the result meant Mr Ross' position was not tenable.