The leader of the country's biggest trade union has written to the Prime Minister urging him to accept a "measure of agreement" over controversial plans to introduce new thresholds for industrial action ballots.
Len McCluskey, general secretary of Unite, offered to accept thresholds in ballots for strikes in return for secret, secure workplace voting.
The Unite leader called for the adoption of the existing system of union recognition ballots, which has been in place since 2000, as the solution to concerns about thresholds.
Unions have mounted campaigns against a Trade Union Bill, currently going through Parliament, which introduces a 50% threshold for strike ballots and changes to picketing and union funds.
Unite said that opposition to the Bill was growing and now included the police, human resource managers, civil liberties groups and even Conservative MPs.
The Government was accused of failing to make a sensible case for the new law and was in increasing danger of being seen to be mounting little more than an "ideological attack" on unions.
In his letter to David Cameron, Mr McCluskey said: "I am aware that government ministers and you yourself have justified the introduction of this measure by reference to concerns over low turnouts in some ballots leading to strike action. No-one, of course, can be happy when strike action takes place - especially in services on which the public depend - on the basis of the active endorsement of only a minority of trade union members affected. In my long experience of industrial relations, mainly in the private sector, such strikes are a rarity.
"Were you to be able to accept this modern and democratic proposal to update balloting procedures then Unite, for its part, would be comfortable about accepting the thresholds and the time limit on the validity of ballots proposed in the Trade Union Bill, without prejudice to our position on other elements of the legislation.
"Nevertheless, since I assume you are sincere about the concerns you raise about turnout, I would ask you to give urgent consideration to amending the Bill before parliament in order to permit the introduction of more modern methods of balloting including online, digital and, most importantly, secure and secret balloting in the workplace.
"I very much hope you will respond to this proposal in the spirit with which it is intended."
Mr Cameron said the prospect of agreement on thresholds was "interesting".
Speaking on BBC One's The Andrew Marr Show, he said: "The trade unions are accepting these thresholds are right, that you shouldn't have damaging strikes that close schools or shut hospitals or stop underground systems working, you shouldn't have those things without a proper turnout of voters."
But he added: "The Speaker of the House of Commons did put together a commission to look at electronic voting and the conclusion of that commission was that it wasn't safe from fraud. So I think there are problems with that approach."
The Prime Minister continued: "Is it really too much to ask someone who is going to go on strike, who is going to disrupt people's children's school, to fill in a ballot paper to do that?"
Mr Cameron suggested controversial parts of the Bill such as a requirement for people on pickets to wear armbands and to have social media posts vetted in advance could be reviewed.
"All these measures in the legislation can be discussed as they go through Parliament," he said.
"The heart of the legislation is thresholds so you can't have strikes based on a ballot sometimes years before the actual strike takes place, based on very low turnouts.
"That's the heart of the Bill, that's what's being proposed. A lot of other stuff you read is frankly not in the Bill."
On never meeting Mr McCluskey, Mr Cameron said: "I've met the TUC in my office, they can bring who they like frankly."
TUC general secretary Frances O'Grady denied claims by the Prime Minister that the TUC had met Number 10 over the Bill.
"Not true. I wrote to him just after the election, but still no reply," she tweeted.