The Prime Minister urged medics “at this late stage” to get back around the table before the proposed walkout, which starts at 8am tomorrow.
He said: “This strike is not necessary, it will be damaging.
“We are doing everything we can to mitigate its effects but you can’t have a strike on this scale in our NHS without there being some real difficulties for patients and potentially worse.”
Mr Cameron’s official spokeswoman also told a Westminster media briefing: “We are concerned about the situation. We are doing everything we can to ensure that patient safety is protected and to provide the urgent care that patients need.
“So there have been a number of contingency planning meetings in the run-up to this strike going ahead. The Department of Health will be closely monitoring the situation and working with NHS England on that.”
Earlier, NHS England said hospitals will be under “additional pressure” as thousands of junior doctors go on strike in the dispute over pay and a new contract.
Around 100 picket lines are being put in place for Tuesday’s strike, with a large concentration in and around London.
NHS England said 1,425 inpatient operations and procedures were being cancelled as a result of the strike along with 2,535 outpatient ones.
It said there are around 4,000 cancellations in total, of which 3,400 are on Tuesday.
Some 654 cancellations - 192 inpatients and 462 day cases - are in London.
Labour leader Jeremy Corbyn has said it is vital that an agreement is reached “quickly” in the dispute, which could lead to four days of industrial action in all.
In advice to patients, NHS England said: “Urgent and emergency care services will be available as normal but hospitals are expected to be under additional pressure.
“Where possible, people should contact their GP, seek advice from their local pharmacist, call NHS 111 or consult the NHS Choices website.”
It added: “People should be particularly attentive to their health over this period and look out for more vulnerable members of their families and communities.”
Talks aimed at resolving the dispute over a new contract failed on Friday, although further talks will continue.
Junior doctors are set to provide emergency care only for 24 hours from 8am on Tuesday.
This will be followed by a 48-hour stoppage and the provision of emergency care only from 8am on January 26.
On February 10, there will be a full withdrawal of labour from 8am to 5pm.
Mr Corbyn told the BBC Radio 4 Today programme: “We should recognise that junior doctors are qualified, extremely hard-working, deserve to be treated properly and (Health Secretary) Jeremy Hunt should now come to an agreement with them.”
He added: “I hope that Jeremy Hunt realises the need to come to an agreement very quickly.”
The basis for the current round of negotiations is the Government’s offer from early November, including an 11% rise in basic pay for junior doctors.
This is offset by plans to cut the number of hours on a weekend for which junior doctors can claim extra pay for unsocial hours.
Currently, 7pm to 7am Monday to Friday and the whole of Saturday and Sunday attract a premium rate of pay.
Under the Government’s offer, junior doctors would receive time-and-a-half for any hours worked Monday to Sunday between 10pm and 7am, and time-and-a-third for any hours worked between 7pm and 10pm on Saturdays and 7am and 10pm on Sundays.
The BMA has said there are still several areas of dispute, despite Mr Hunt saying the only sticking point is weekend pay.
England’s Chief Medical Officer, Dame Sally Davies, said on Sunday that the strike would “lead to patients suffering”.
Jonathan Isaby, chief executive of the TaxPayers’ Alliance, said: “The BMA should call off this dangerous strike and return to the negotiating table before patients suffer, not least because they insist that patient safety is their paramount concern.”
In an interview over the weekend, Mr Hunt said the Government was going through the “exhaustive process” of contacting every A&E department in the country to establish whether they would have enough staff to stay open.
But he admitted “hospitals are stretched at the moment”.
Unite head of health Barrie Brown said: “The fact that Hunt - who has been more critical of NHS staff than any health secretary since 1948 - has allowed matters reach this stage is a disgrace, and he needs to enter into meaningful and constructive talks with the junior doctors as a matter of urgency.
“Unite’s 100,000 members in the health service will be giving the doctors maximum support within the bounds of the law by joining protests outside their working hours and taking to social media to highlight their support.
“The fact that this is the first industrial action by doctors since 1975 demonstrates the cack-handed and ideological way that ministers have dealt with the NHS since 2010 - the chickens have come home to roost.”
RMT general secretary Mick Cash said: “RMT stands in full support of our junior doctors as they prepare to take industrial action in defence of the basic principle of decent working conditions for NHS staff who work round the clock saving lives.
“RMT members are urged to join the picket lines at their local hospital tomorrow to show solidarity with the junior doctors at this crucial point in their fight for justice.”