In an interview on Sunday with Laura Kuenssberg, Streeting said the strike action had "little to no public support", and would be "inflicting more harm and delays to patients".
He added that the deal, which does not include negotiating on pay rises, remained on the table.
But he 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."
The strike - the 13th in the pay dispute since March 2023 - is expected to cause significant disruption, including in hospitals.
The BMA and the government have been in dialogue throughout the summer and early autumn since the last walkout at the end of July, but talks broke down earlier this month.
Streeting has maintained he would not negotiate on pay after resident doctors, the new name to junior doctors, received pay rises totalling nearly 30% in the past three years.
Talks had instead focused on career progression, working conditions and out-of-pocket expenses like exam fees.
But the union argues that resident doctors' pay is still a fifth lower than it was in 2008, once inflation is taken into account.