diff --git a/.lintr b/.lintr
index fbe54d2ce..8420e7ba5 100644
--- a/.lintr
+++ b/.lintr
@@ -1,5 +1,5 @@
 linters: all_linters(
-    backport_linter("3.6.0", except = c("R_user_dir", "deparse1", "...names")),
+    backport_linter("auto", except = c("R_user_dir", "deparse1", "...names")),
     line_length_linter(120L),
     object_overwrite_linter(allow_names = c("line", "lines", "pipe", "symbols")),
     todo_comment_linter(
diff --git a/R/backport_linter.R b/R/backport_linter.R
index a285c7e39..e35f7f055 100644
--- a/R/backport_linter.R
+++ b/R/backport_linter.R
@@ -5,6 +5,8 @@
 #' @param r_version Minimum R version to test for compatibility. Defaults to
 #'  the R version currently in use. The version can be specified as a version
 #'  number, or as a version alias (such as `"devel"`, `"oldrel"`, `"oldrel-1"`).
+#'  It can also be `"auto"` to use the minimum R version declared in the
+#'  `DESCRIPTION` file of R packages.
 #' @param except Character vector of functions to be excluded from linting.
 #'  Use this to list explicitly defined backports, e.g. those imported from the `{backports}` package or manually
 #'  defined in your package.
@@ -120,6 +122,15 @@ normalize_r_version <- function(r_version) {
     ))
 
     r_version <- R_system_version(available_patches[selected_patch])
+  } else if (identical(r_version, "auto")) {
+    r_version <- min_r_version()
+    if (is.na(r_version)) {
+      cli_warn(c(
+        x = "No DESCRIPTION file or no specified minimum R version could be found.",
+        i = "Setting {.arg r_version} to the currently running R version (R {getRversion()})."
+      ))
+      r_version <- getRversion()
+    }
   } else if (is.character(r_version)) {
     r_version <- R_system_version(r_version, strict = TRUE)
   } else if (!inherits(r_version, "R_system_version")) {
diff --git a/R/settings_utils.R b/R/settings_utils.R
index 166dd362a..f114ce415 100644
--- a/R/settings_utils.R
+++ b/R/settings_utils.R
@@ -112,3 +112,23 @@ pkg_name <- function(path = find_package()) {
   nm <- read.dcf(file.path(path, "DESCRIPTION"), fields = "Package")[1L]
   if (!is.na(nm)) nm
 }
+
+min_r_version <- function(path = find_package(".")) {
+  if (is.null(path)) {
+    return(NA_character_)
+  }
+  depends_field <- read.dcf(file.path(path, "DESCRIPTION"), fields = "Depends")
+
+  depends <- trimws(strsplit(depends_field, ",", fixed = TRUE)[[1L]])
+
+  min_r_ver <- gsub("^R \\(>=?\\s(.+)\\)", "\\1", grep("R ", depends, value = TRUE, fixed = TRUE))
+
+  if (length(min_r_ver) == 0) {
+    return(NA_character_)
+  }
+  # According to 'Writing R Extensions', the trailing 0 for patch version can
+  # be dropped.
+  # But we want to identically match an existing version number so we add it if
+  # it's missing.
+  gsub("^(\\d+\\.\\d+)$", "\\1.0", min_r_ver)
+}
diff --git a/man/backport_linter.Rd b/man/backport_linter.Rd
index 22c97ebbe..64bfd3ac9 100644
--- a/man/backport_linter.Rd
+++ b/man/backport_linter.Rd
@@ -9,7 +9,9 @@ backport_linter(r_version = getRversion(), except = character())
 \arguments{
 \item{r_version}{Minimum R version to test for compatibility. Defaults to
 the R version currently in use. The version can be specified as a version
-number, or as a version alias (such as \code{"devel"}, \code{"oldrel"}, \code{"oldrel-1"}).}
+number, or as a version alias (such as \code{"devel"}, \code{"oldrel"}, \code{"oldrel-1"}).
+It can also be \code{"auto"} to use the minimum R version declared in the
+\code{DESCRIPTION} file of R packages.}
 
 \item{except}{Character vector of functions to be excluded from linting.
 Use this to list explicitly defined backports, e.g. those imported from the \code{{backports}} package or manually