The Scottish Conservative leader called on her party to rethink its stance and lead a “mature” debate on immigration that balances the economic benefits and pressures that migration brings to the UK.
Opponents claimed the Tories were in “open warfare” over the UK’s immigration target after senior cabinet figures appealed to the Prime Minister to ease the target earlier this year.
Her comments will be seen a challenge to Mrs May and an endorsement of potential successors such as Home Secretary Amber Rudd, who was among those to cast doubt over whether the 100,000 target would be maintained.
Ms Davidson and Ms Rudd are believed to have held a private meeting in Glasgow last week amid growing speculation that the Scottish Conservative leader’s popularity among grassroots party members could make her an influential figure in a future leadership contest.
Writing in the Daily Telegraph, Ms Davidson highlighted the government’s failure to bring net migration down to the tens of thousands in any year since the target was adopted in 2010.
“Brexit is a big reset button and should - in theory - make that much easier to do so. But we have to ask whether the target continues to be the right one?” she wrote.
Falling unemployment and a shrinking workforce means reducing migration could harm the economy in the long term, Ms Davidson argued.
And she said international students, who made up more than half of the 273,000 net migration total for the year to September 2016, should no longer be included in figures in order to ease public fears that immigration is too high.
Ms Davidson said: “The great problem is that the two principles of our immigration policy - public trust and business need for skilled foreign workers - appear to be in conflict. But they don’t need to be.
“According to the pollster ComRes, only 24 per cent of British adults think that international students are immigrants.
“More than 90 per cent say international students should be able to work in the UK for a period of time after they have completed their study.
“So let’s start there. If people don’t think that students should be included in the net migration numbers, let’s take them out.”
The Prime Minister has repeatedly rejected calls from business and leading figures in her own party for students to be stripped out of net migration figures.
Ms Davidson also challenged a key plank of Mrs May’s record as Home Secretary, arguing that international students should have longer to look for work in the UK after they finish their courses.
The tier 1 (post-study work) visa was abolished by Mrs May’s department in 2012, despite calls for a reprieve from business and the university sector.
Following the Conservatives’ election setback in June, Ms Davidson issued a further warning to her colleagues in government, arguing the Tories need to strike a more conciliatory tone on immigration to see off the threat from a resurgent Labour Party.
“Many of those voting groups we need to reconnect with - younger voters, those in urban areas - are more likely to be either immigrants themselves or have a number of non-British nationals within their family or social groups,” she said.
“For a start, we could get the message out more clearly that there is nothing so Conservative as pulling your loved ones close and striving to build a better future for your family, which is what so many immigrants do.”
She ended the article: “The time for easy slogans is over. Let’s treat the British public like the grown ups they are and have the mature conversation we need.”
Downing Street did not respond to the article.
Labour shadow Scotland Office minister Paul Sweeney said: “The Tories are in open warfare and these comments from Ruth Davidson show just deep the splits in the party run.
“When the leader of the Scottish Conservatives, who defends abhorrent policies such as the rape clause, tells Theresa May that she needs to think again then you know just how wrong the Prime Minister is.
“Our elderly population is expected to grow significantly, while the working-age population is forecast to increase only marginally, which shows just how wrong-headed the Tory approach on immigration is.”
The SNP said Ms Davidson, who backed Remain in the EU referendum, had committed another “U-turn” and called on the Prime Minister to follow suit.
Immigration spokesman Stuart McDonald MP said: “Brexit threatens to be economically disastrous for Scotland, and it seems Ruth Davidson is only now waking up to that fact.
“But the person who needs to be persuaded is her boss in Downing Street, Theresa May – and the PM shows no sign of ditching her reckless pursuit of a hard Brexit.”