Labour leader Ed Miliband has offered Liberal Democrats the chance to take part in Labour's policy review.
He said many Lib Dems were "ashamed" by the direction of the coalition.
Echoing Tony Blair's quote after 9/11, Mr Miliband said the "kaleidoscope" of British politics had been shaken, but the pieces had not yet settled.
Lib Dem Tim Farron said Labour spent years "sucking up to Rupert Murdoch and George Bush - why would any progressive even give them a second glance?"
Mr Farron, the party's president-elect, added: "Liberal Democrats have started fixing Labour's economic mess, taking millions of people out of income tax and reforming British politics.
"Continuing that work is something far more attractive to Liberal Democrats than helping Ed Miliband's increasingly desperate attempts to work out what he actually stands for."
Addressing journalists at his first monthly media conference as Leader of the Opposition he said it was clear that when David Cameron made his "big, open and comprehensive" offer to Lib Dem leader Nick Clegg to form the coalition, his "real purpose was to use them to justify an economic agenda" of the right.
Mr Miliband said he wanted to "maximise" Labour's vote in the elections next year but added: "What I also recognise is to coin a phrase, the kaleidoscope of British politics has been shaken and I don't think the pieces have properly settled."
He said he believed there was a split in the Liberal Democrats between the "orange book" followers on the right and those on the left and centre of the party.
He said he had asked Liam Byrne, who is heading up Labour's policy review, to work with Richard Grayson - a former policy chief for the Lib Dems - to "draw up areas where our policy reviews can be informed by submissions and ideas of Liberal Democrats who want to contribute".
"To Liberal Democrats who fear their deal with the Tories is shifting the gravity of British politics to the right, I invite them to work with us against the direction in which this government is taking Britain."
He highlighted "areas of common interest" - social mobility, the economy and "the way we do our politics".
He raised the issue of education maintenance allowance - aimed at encouraging poorer pupils to stay in education - which he described as a ladder "being kicked away by this government".
Ministers say the scheme, worth up to £30 a week, is inefficient.
On the economy he said the coalition was "sacrificing everything on the altar of deficit reduction". And he said despite claims to a "new politics" - David Cameron and Nick Clegg were guilty of some of the worst examples of the "old politics" - having broken promises on child benefit, knife crime and tuition fees.
"There are many people in that party who are deeply frustrated and even ashamed at the way their progressive tradition has been hijacked by the coalition," he said.
During the Labour leadership campaign, Mr Miliband reportedly said he had "a plan to make the Lib Dems an endangered species, and then extinct". Asked whether Lib Dems should be suspicious of his offer he said he made those comments when "in a meeting in Scotland talking about a specific fight with the Liberal Democrats in the local elections".
Door open for brother
He was also asked about comments he had made that he would only work with the Lib Dems in a hung parliament if Nick Clegg stood down as leader. He said the Liberal Democrats had "to take care of themselves", but he would find it "very difficult" to work with Mr Clegg.
Asked if he would consider an electoral pact - where Labour would not challenge the Lib Dems in some seats - he said: "That's slightly getting ahead of ourselves, my aim for the next election is... I would like a majority Labour government. But in the meantime I think for us to talk to people outside our party is a good thing."
Mr Miliband narrowly beat his older brother David to the party leadership - David Miliband told his local paper, the Journal, on Monday he had "no plans to return to front line politics - at the moment, that is".
But he added: "I've got to admit I wish the leadership campaign had gone differently but who knows what will happen in the future?"
Ed Miliband said he would "very much welcome him returning" and his "door was always open" - adding he would look at the interview to see "exactly what he said".
On Sunday Lib Dem deputy leader Simon Hughes said: "My plea to people in the party and outside - who might be concerned at the moment as to where we are going - is 'stay with us' because progressives are needed more now than ever in history of the party."
And former Conservative Prime Minister Sir John Major said suggestions Labour would "reach out" to unhappy Lib Dems - made his "blood boil". He said the Conservatives and Lib Dems had come together in the national interest and said this was not a time "to be playing party games".