He said: "I don't think I've met anybody who doesn't want to sign it," he said.
Tory leader Davidson said: "Sadly, it's no surprise that someone found guilty of conducting a campaign of violence against women is refusing to do the right thing and resign his post."
He said: "We cannot allow a wife beater to take his place back in Parliament as if nothing has happened.
beater Bill Walker defies calls to stand down from his Holyrood seat
While a majority of MSPs at Holyrood have backed his motion, Mr Rennie said he hoped more would sign it in the coming days.
Rennie told BBC Radio Scotland it was time for Walker to stand down.
The Scottish Parliament is due to resume next week following the summer recess and Walker said: "I never had any plans to vacate my seat and that's it. I will just leave it at that."
But in summary cases heard in sheriff courts in Scotland, the maximum sentence that can be handed down is one year, allowing Walker to remain as an MSP.
believe that Bill Walker cannot represent them any more".
"We're still in recess just now and I think by the time we get back next week we will have almost everybody backing Nike Air Max 2015 Mens Shoes
The Scottish Parliament website showed that 66 MSPs have backed a motion from Liberal Democrat leader Willie Rennie, stating: "The Parliament believes that Bill Walker MSP should vacate his seat in the Parliament immediately."
First Minister Alex Salmond called on him to resign his Holyrood seat, saying: "Someone convicted of these offences is not fit to Nike Air Max Tavas Essential Black White
"To make matters worse, his determination to remain an MSP could end up costing the taxpayer hundreds of thousands of pounds.
"And that would be the message it would send to all these women who have been beaten up by their partner? What would they think about their Parliament acting in that way?"
Rennie said he had already had people from Walker's constituency of Dunfermline contact him instead of their MSP "because they Air Max Tavas Black Cool Grey
Politicians from across the spectrum have demanded Walker stand down from Holyrood after the independent MSP was convicted of 23 assaults and one breach of the peace charge.
On that basis, the Liberal Democrat leader said Walker "can't do his job, he can't function as an MSP".
be a public representative and therefore he should stand down from the Nike Air Max 2015 Running Scottish Parliament and allow the people of Dunfermline to elect a new MSP."
He carried out the attacks against his three ex wives and a stepdaughter between 1967 and 1995.
"Ultimately, it is for Bill Walker to examine his conscience and decide if he thinks it would be right to take a large sum of public money from a situation caused by his own misdemeanours.
Walker is due to be sentenced next month after being found guilty of 24 charges spanning almost three decades following a trial at Edinburgh Sheriff Court.
The law states that any elected member jailed for more than one year will be disqualified.
The Tory leader added: "It is appalling that Bill Walker thinks he can just carry on as an elected member of parliament as if nothing has happened.
The former SNP MSP, who was ejected from the party when the allegations surfaced, denied the charges.
Politicians from all parties at Holyrood have signed this, including Labour leader Johann Lamont, Tory leader Ruth Davidson and her deputy Jackson Carlaw.
DISGRACED MSP Bill Walker is to defy calls to quit despite being convicted of a series of attacks on three of his ex wives.
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