Replace NA values of data.frame based on multiple conditions by values same data.frame

Question

consider the following data.frame:

df1 <- data.frame(index = c(1,1,1,2,2,2),
                  country = c("AR","AR", "DE", "CH", "AR", "DE"),
                  type = c("CoL", "CPI", "GDP", "CPI", "CPI", "GDP"),
                  value = c(11.12, 53.32, 10.42, 120.23, NA, NA))
> df1
  index country type  value
1     1      AR  CoL  11.12
2     1      AR  CPI  53.32
3     1      DE  GDP  10.42
4     2      CH  CPI 120.23
5     2      AR  CPI     NA
6     2      DE  GDP     NA

How can I replace NAs by the corresponding value of previous index, but only if all other attributes except for index match each other, so the result would look like this:

> df2
  index country type  value
1     1      AR  CoL  11.12
2     1      AR  CPI  53.32
3     1      DE  GDP  10.42
4     2      CH  CPI 120.23
5     2      AR  CPI  53.32
6     2      DE  GDP  10.42

Since the actual data.frames are quite big I intend to avoid using for loops to screen the data multiple times.
Thanks folks!