Tata Steel plans to sell its UK plants, which employ 15,000 people - 6,000 in Wales - and support thousands more.
Mr Jones will call for the Welsh plants to be taken into "public ownership" until a buyer is found. The PM has said nationalisation is not the answer.
Business Secretary Sajid Javid is due to fly to India later to discuss the sale process with Tata's chairman.
Beforehand, Mr Javid is due to meet union representatives, when he will be urged to back their plan for the future of the Tata sites.
Tata has plants in Wales at Port Talbot, Llanwern and Orb in Newport, Shotton in Flintshire and Trostre in Llanelli. The company also has sites in England, including Scunthorpe, Rotherham and Corby.
Mr Javid, who has faced criticism for his handling of the issue, said he held "productive" talks with Tata executives on Monday, saying that progress had been made.
He will attend the London meeting between Mr Jones and Mr Cameron, along with Welsh Secretary Alun Cairns and Chancellor George Osborne.
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Mr Jones said he had a simple message to the prime minister that the plants must not close.
"Britain must remain a steel producing country and we must work together to achieve and maintain that," he said.
"The Welsh Government has committed to doing what we can within our available powers and resources, and now its time for the UK government to act.
"There are strong economic, moral and strategic reasons why we must continue to produce our own steel, and I will be making that argument very clearly, as well as asking for solidarity and support for our workforce.
"I will be asking the PM to provide assurance that the UK government will take Tata's plants in Wales into public ownership to allow enough time for a buyer to be found."
Mr Cameron said: "At this morning's meeting, Carwyn Jones and I will look at how London and Cardiff can work together to make sure that the Port Talbot plant has a solid future and end the uncertainty for workers and their families.
"We remain fully focused on finding a buyer to run the steelworks and today's meeting is an opportunity to discuss what needs to be done to make this prospect as attractive as possible to investors."
Tata Steel has said there is "no fixed timeline" for the sale process but stressed that urgency is needed to avoid "a long period of uncertainty" for employees and customers.
Former deputy PM Nick Clegg has called for the government to assist with Tata's pension liabilities.
He told BBC Radio 4's Today programme: "There has to be some government intervention, directly or indirectly, to lighten the burden of the pension liability with any new buyer."
Tata had a long-term future if the issue of cheap Chinese steel imports were addressed, he said, and it was "legitimate" for the government "to step in to help" as it had done with pension liabilities at Royal Mail.
Last week, Mr Cameron said the UK government was working to save thousands of steel jobs but warned there was "no guarantees of success". He also said nationalisation was not the right answer.
Labour leader Jeremy Corbyn has accused the Conservatives of having an "ideological allergy to public ownership".
The union plan involves securing the customer base by guaranteeing production at Tata sites, not allowing Tata or other buyers to "cherry pick" parts of the business, and offering government support for two to three years while the industry gets "back to self-sustainability".
Potential buyer Sanjeev Gupta, head of the Liberty Group, said on Monday he could take over all of the business without mass job losses.
He said he had "very encouraging" talks with the UK government but there was still a lot of work to do.
Meanwhile the assembly's enterprise and business committee is meeting to discuss the steel crisis on Tuesday.
It will take evidence from Economy Minister Edwina Hart, representatives of Tata and Cardiff-based Celsa Steel, union officials and Neath Port Talbot council chief executive Steve Phillips.
Wales First Minister Carwyn Jones and UK PM David Cameron are discussing how to save thousands of steel jobs.