Resident doctors in England are due to take five days of strike action between 14-19 November.
The BMA has said Streeting could prevent strikes 'by bringing credible proposals to the table and not play[ing] politics with doctors who dedicate their lives to the health of the nation'.
In an interview on Sunday with Laura Kuenssberg, Streeting said there was a deal available to increase the number of speciality training places and provide support for expenses, such as exam fees.
He said the strike action had 'little to no public support', and would be 'inflicting more harm and delays to patients'.
Streeting told the programme: 'What we will not do, however, is be held to ransom and what I will not do is allow those costs of strikes to be inflicted on other NHS staff who are working constructively with us, or on patients in terms of the services that they receive.'
He said the current offer, which would provide additional training places and help with out-of-pocket expenses, would 'be a win-win scenario where together we motor ahead with the progress we're making in the NHS'.
Following the programme, a DHSC spokesperson, said: ‘This government has delivered a record-breaking £29bn investment in our NHS – including up to £10bn on digital and technology transformation and £750m for urgent capital repairs – demonstrating our unwavering commitment to properly funding the health service that we all rely on.
‘We know that needless strikes will divert money, time and resourcing away from the front line. That's why the health secretary has urged the BMA to stop being selfish and start putting patients first.'
Meanwhile, in an interview with Newcross Healthcare's Voices of Care podcast, former health secretary Sir Jeremy Hunt said Streeting may have thought NHS strikes happened because of ‘hopeless evil Tories' but warned there are ‘very politically motivated people' within health unions who will demand more.
