diff --git a/NEWS.md b/NEWS.md
index 9163d9eb3f..db9ab2dee3 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -42,6 +42,8 @@
 
 13. `dcast`gains `value.var.in.dots`, `value.var.in.LHSdots` and `value.var.in.RHSdots` arguments, [#5824](https://github.com/Rdatatable/data.table/issues/5824). This allows the `value.var` variable(s) in `dcast` to be represented by `...` in the formula (if not otherwise mentioned). Thanks to @iago-pssjd for the report and PR.
 
+14. `all.equal.data.table` gains `ignore.indices` argument, [#6134](https://github.com/Rdatatable/data.table/issues/6134).
+
 ## BUG FIXES
 
 1. `unique()` returns a copy the case when `nrows(x) <= 1` instead of a mutable alias, [#5932](https://github.com/Rdatatable/data.table/pull/5932). This is consistent with existing `unique()` behavior when the input has no duplicates but more than one row. Thanks to @brookslogan for the report and @dshemetov for the fix.
diff --git a/R/setops.R b/R/setops.R
index 23dd6ec8f6..b455fffc07 100644
--- a/R/setops.R
+++ b/R/setops.R
@@ -104,8 +104,8 @@ fsetequal = function(x, y, all=TRUE) {
 
 # all.equal ----
 
-all.equal.data.table = function(target, current, trim.levels=TRUE, check.attributes=TRUE, ignore.col.order=FALSE, ignore.row.order=FALSE, tolerance=sqrt(.Machine$double.eps), ...) {
-  stopifnot(is.logical(trim.levels), is.logical(check.attributes), is.logical(ignore.col.order), is.logical(ignore.row.order), is.numeric(tolerance), is.data.table(target))
+all.equal.data.table = function(target, current, trim.levels=TRUE, check.attributes=TRUE, ignore.indices=FALSE, ignore.col.order=FALSE, ignore.row.order=FALSE, tolerance=sqrt(.Machine$double.eps), ...) {
+  stopifnot(is.logical(trim.levels), is.logical(check.attributes), is.logical(ignore.indices), is.logical(ignore.col.order), is.logical(ignore.row.order), is.numeric(tolerance), is.data.table(target))
 
   if (!is.data.table(current)) {
     if (check.attributes) return(paste0('target is data.table, current is ', data.class(current)))
@@ -163,20 +163,23 @@ all.equal.data.table = function(target, current, trim.levels=TRUE, check.attribu
       ))
     }
     # check index
-    i1 = indices(target)
-    i2 = indices(current)
-    if (!identical(i1, i2)) {
-      return(gettextf(
-        "Datasets have different %s. 'target': %s. 'current': %s.",
-        "indices",
-        if(length(i1)) brackify(i1) else gettextf("has no index"),
-        if(length(i2)) brackify(i2) else gettextf("has no index")
-      ))
+    if (!ignore.indices) {
+      i1 = indices(target)
+      i2 = indices(current)
+      if (!identical(i1, i2)) {
+        return(gettextf(
+          "Datasets have different %s. 'target': %s. 'current': %s.",
+          "indices",
+          if(length(i1)) brackify(i1) else gettextf("has no index"),
+          if(length(i2)) brackify(i2) else gettextf("has no index")
+        ))
+      }
     }
 
     # Trim any extra row.names attributes that came from some inheritance
     # Trim ".internal.selfref" as long as there is no `all.equal.externalptr` method
-    exclude.attrs = function(x, attrs = c("row.names",".internal.selfref")) x[!names(x) %chin% attrs]
+    # Trim "index" attribute, in case `ignore.indices` is set (if it is not, we already checked it).
+    exclude.attrs = function(x, attrs = c("row.names",".internal.selfref", "index")) x[!names(x) %chin% attrs]
     a1 = exclude.attrs(attributes(target))
     a2 = exclude.attrs(attributes(current))
     if (length(a1) != length(a2)) return(sprintf("Datasets has different number of (non-excluded) attributes: target %s, current %s", length(a1), length(a2)))
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index 021b3f19e7..04aa5c4017 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -8684,6 +8684,7 @@ DT1 <- data.table(a = 1:4, b = letters[1:4])
 DT2 <- data.table(a = 1:4, b = letters[1:4])
 setindexv(DT1, "b")
 test(1613.25, all.equal(DT1, DT2), "Datasets have different indices. 'target': [b]. 'current': has no index.")
+test(1613.251, all.equal(DT1, DT2, ignore.indices = TRUE), TRUE)
 test(1613.26, all.equal(DT1, DT2, check.attributes = FALSE), TRUE)
 test(1613.27, all.equal(DT1, setindexv(DT2, "a")), "Datasets have different indices. 'target': [b]. 'current': [a].")
 test(1613.28, all.equal(DT1, setindexv(DT2, "b")), "Datasets have different indices. 'target': [b]. 'current': [a, b].")
@@ -8693,6 +8694,7 @@ DT1 <- data.table(a = 1:4, b = letters[1:4])
 DT2 <- data.table(a = 1:4, b = letters[1:4])
 setattr(DT1, "custom", 1L)
 test(1613.30, all.equal(DT1, DT2), "Datasets has different number of (non-excluded) attributes: target 3, current 2")
+test(1613.301, all.equal(DT1, DT2, ignore.indices = TRUE), "Datasets has different number of (non-excluded) attributes: target 3, current 2")
 test(1613.31, all.equal(DT1, DT2, check.attributes = FALSE), TRUE)
 setattr(DT2, "custom2", 2L)
 test(1613.32, all.equal(DT1, DT2), "Datasets has attributes with different names: [custom, custom2]")
diff --git a/man/all.equal.data.table.Rd b/man/all.equal.data.table.Rd
index 44d9a29037..a89bcd87ad 100644
--- a/man/all.equal.data.table.Rd
+++ b/man/all.equal.data.table.Rd
@@ -8,8 +8,8 @@
 
 \usage{
   \method{all.equal}{data.table}(target, current, trim.levels=TRUE, check.attributes=TRUE,
-    ignore.col.order=FALSE, ignore.row.order=FALSE, tolerance=sqrt(.Machine$double.eps),
-    \dots)
+    ignore.indices=FALSE, ignore.col.order=FALSE, ignore.row.order=FALSE,
+    tolerance=sqrt(.Machine$double.eps), \dots)
 }
 
 \arguments{
@@ -27,6 +27,10 @@
     A logical indicating whether or not to check attributes, will apply not only to data.table but also attributes of the columns. It will skip \code{c("row.names",".internal.selfref")} data.table attributes.
   }
 
+  \item{ignore.indices}{
+    A logical indicating whether or not to ignore if tables differ by indices. Since \code{data.table} indices are attributes, \code{ignore.indices} is implied when \code{check.attributes} is FALSE.
+  }
+
   \item{ignore.col.order}{
     A logical indicating whether or not to ignore columns order in \code{data.table}.
   }