In a letter to England's directors of children's services, minister for children and families Robert Goodwill said the extra £1m would increase the amount of money available in 2017/18 through the fund to £29m.
"Demand for the fund continues to grow and is almost three times the level it was in 2015/16," wrote Goodwill. "In recognition of that rising demand, I am pleased to announce that an additional £1m will be made available this year."
Goodwill also confirmed that the department was committed to the fund continuing in the 2018/19 and 2019/20 financial years.
Introduced in May 2015, the fund pays for therapeutic services and other support for adopted children, including inter-country adoptions, and those in special guardianship arrangements.
A total of £52m has been spent through the fund since it launched in May 2015, but a report published by the Department for Education in August found demand for support was so high that some therapeutic services were struggling to keep up.
In 2015, the government introduced per-child funding caps of £2,500 for specialist assessments and £5,000 for therapy, and a recent survey by Adoption UK found that more than two-thirds of respondents believed they required more support to meet their families' needs.
Sue Armstrong Brown, chief executive of Adoption UK, said: "Whilst more money would be welcome, it shows the message - that more support is needed - is being heard by government."
In his letter to directors of children's services, Goodwill confirmed the funding caps would remain in place until the end of the 2019/20 financial year. He urged local authorities to "match fund" money provided through the support fund "where this is necessary to meet children's needs".
He also asked councils to ensure families receive support in a timely manner.
"I continue to hear concerns from some parents and the voluntary sector about delays securing assessments of adoption support needs," he said.
Since its launch, the Adoption Support Fund has contributed to the support of more than 25,500 children.