Ms Davidson, who returns to work from maternity leave this week, said the majority of Scots do not want another poll on the issue.
First Minister Nicola Sturgeon last week said another independence referendum should be held before the next Holyrood elections in 2021.
Westminster has repeatedly refused to countenance such a vote but Ms Sturgeon said “surging” support for independence could help to bring about a change.
Ms Davidson was asked about the UK Government agreeing to a new referendum in a BBC Scotland interview and said: “I’ll say no and this Prime Minister and the next prime minister should say so too.”
The Scottish Conservatives leader will return to work on Thursday ahead of her party’s weekend conference in Aberdeen.
Her deputy Jackson Carlaw has been leading the party in her absence.
Ms Davidson said she does not agree with re-running a referendum Ms Sturgeon said would last for a generation.
She told the BBC: “Nicola Sturgeon doesn’t agree with Nicola Sturgeon on this.
“Not only is she going back on the Edinburgh Agreement that she signed, where she said she would respect the result for a generation, the test she put down for any future referendum before the last election was that a majority of Scots would want it.
“The majority of Scots don’t want this, and if the majority of Scots need a voice to stand up to Nicola Sturgeon, then I will be that voice.
“I don’t agree with re-running a referendum in which the main signatories - including as it happens Nicola Sturgeon - said it would last for a generation.
“She’s done everything she can to rip that agreement up since then.”
She added: “I’m a Conservative and unionist, I will be campaigning to keep the United Kingdom together and honour the result that over two million Scots made in that referendum.”
On Brexit, Ms Davidson said parties need to work together and find a compromise.
She said: “My message to colleagues both in my party and others is now is the time, instead of sticking in your trenches and hoping everyone moves to you, is to take that first step forward and start that compromise that clearly needs to happen.
“We’ve got two sets of people in their trenches shouting at each other - on one side, people demanding a second referendum and on the other demanding a no-deal Brexit.
“And actually for the country, the place where we can coalesce is somewhere in the middle.
“That’s where I’m hoping we can get to and where I’m encouraging colleagues to get to.”
Keith Brown, SNP depute leader, said: “Support for independence is on the rise, and the Tories are clearly running scared - that is what lies behind their utterly undemocratic move to block the people of Scotland having a say.
“That is completely indefensible, and will prove to be an untenable position for Ruth Davidson’s party.
“In terms of Ms Davidson herself, her comments reek of hypocrisy, given her previous statement that the UK Government ‘shouldn’t block’ an independence referendum.”