He said he was happy to give the PM a copy of his party's manifesto, adding, "or better still an early election so the people of this country can decide".
Mrs May will use a speech on Tuesday to call on parties to "contribute and not just criticise".
She says there are a range of issues on which MPs from different parties agree.
First Secretary of State Damian Green described the post-election change in Mrs May's style of government as a "grown-up way of doing politics".
But Mr Corbyn used the PM's Commons statement on the weekend G20 summit in Hamburg to claim it showed "weakness from this government".
"The government is apparently asking other parties for their policy ideas," he said.
Turning to the prime minister, he said: "If you would like it, I'm very happy to furnish you with a copy of our manifesto or better still, an early election so the people in this county can decide.
"Let's face it, the government has run out of steam at a pivotal time in our county and the world around uncertainty over Brexit, conflict in the Gulf states, nuclear sabre-rattling in North Korea, refugees continuing to flee war and destruction, ongoing pandemics, cross-border terrorism, poverty and inequality and the impact of climate change are the core global challenges of our time.
"Just when we need strong government, we have weakness from this government."
Theresa May's speech is a pitch for cross-party consensus.
"Come forward with your own views and ideas about how we can tackle" the challenges the country faces, Mrs May will say, adding: "We may not agree on everything, but ideas can be clarified and improved and a better way forward found."
Bluntly, it is an explicit acknowledgement of her fragility; her authority and majority shrivelled.
Government sources say it is a mature approach that maintains a commitment to taking on big, difficult and complex challenges; not just Brexit but reform of social care, too, for instance.
Labour says Mrs May's speech proves the Conservatives have "completely run out of ideas" and were reduced to "begging" for policy proposals from them.
But Mrs May insisted the government had "an ambitious agenda to change this country", adding that there were many issues on which she  "would hope we would be able to achieve consensus across this House", such as police and security agencies having the powers they need to deal with the terrorist threats they face.
The exchanges came ahead of Mrs May's speech which will return to the message from her first day in Downing street last July, when she succeeded David Cameron, and vowed to lead what she called a "one nation" government that works for all and not just the "privileged few".
The speech is being seen by some as a "re-launch" or "fightback" after Mrs May lost her majority - and much of her authority - in the snap election last month.
In her speech, the PM will say that although the result of June's election was not what she wanted, "those defining beliefs remain, my commitment to change in Britain is undimmed".
She will unveil a review - of casual and low-paid work - by Matthew Taylor, a former top adviser to Tony Blair, which she commissioned when she became prime minister.
It is thought Mr Taylor, who has been examining the use of zero-hours contracts and the rise in app-based firms such as Uber and Deliveroo, will stop short of calling for a compulsory minimum wage for those employed in the so-called gig economy, who do not have guaranteed hours or pay rates.
But he is expected to propose a series of extra rights for those in insecure jobs and could also recommend shaking up the tax system to reduce the gap between employees and the self-employed.
He is also likely to call for measures to improve job satisfaction for people working in minimum wage jobs, according to The Guardian.
Speaking at a press conference with Australian counterpart Malcolm Turnbull on Monday, Mrs May said she had sought input from other parties in the past on issues like counter-terrorism and modern slavery.
She also said she was happy to work with Labour's Yvette Cooper and others in a cross-party approach to tackling intimidation and online abuse of MPs and others involved in the political process.
Asked if her desire for co-operation extended to Brexit, including on the government's Repeal Bill when it is published later this week, the prime minister said she was seeking the "broadest possible consensus" surrounding the terms of the UK's exit.
Lib Dem Brexit spokesman Tom Brake said: "A call for Labour to contribute is superfluous. On the single biggest issue of our generation, Brexit, Corbyn isn't contributing, he is cheerleading."
Scottish Government Brexit minister Michael Russell said: "If the prime minister is genuinely interested in creating a consensus then Scotland should have a seat at the negotiations to leave the EU."
But Mr Green, who has known Mrs May since university and is effectively her deputy prime minister, said the public would welcome a move away from politics in which parties "just sit in the trenches and shell each other".
The BBC's assistant political editor, Norman Smith, said that the Conservatives and Labour were "poles apart" on many significant policy areas.
He told BBC Radio 4's The World at One: "More brutally, Jeremy Corbyn is not minded to help Theresa May. He smells blood in the water.
"He wants to do everything he can to stampede Mrs May into another election, so the idea he might somehow seek to cooperate with her, I think, is bordering on the fanciful."
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Jeremy Corbyn has said Theresa May's call for rival parties to contribute their policy ideas showed the government "has run out of steam".