diff --git a/datafusion/functions/src/regex/regexplike.rs b/datafusion/functions/src/regex/regexplike.rs
index 20029ba005c4..8cd26a824acc 100644
--- a/datafusion/functions/src/regex/regexplike.rs
+++ b/datafusion/functions/src/regex/regexplike.rs
@@ -48,9 +48,9 @@ impl RegexpLikeFunc {
             signature: Signature::one_of(
                 vec![
                     Exact(vec![Utf8, Utf8]),
-                    Exact(vec![LargeUtf8, Utf8]),
+                    Exact(vec![LargeUtf8, LargeUtf8]),
                     Exact(vec![Utf8, Utf8, Utf8]),
-                    Exact(vec![LargeUtf8, Utf8, Utf8]),
+                    Exact(vec![LargeUtf8, LargeUtf8, LargeUtf8]),
                 ],
                 Volatility::Immutable,
             ),
diff --git a/datafusion/functions/src/regex/regexpmatch.rs b/datafusion/functions/src/regex/regexpmatch.rs
index bf40eff11d30..498b591620ee 100644
--- a/datafusion/functions/src/regex/regexpmatch.rs
+++ b/datafusion/functions/src/regex/regexpmatch.rs
@@ -54,9 +54,9 @@ impl RegexpMatchFunc {
                     // If that fails, it proceeds to `(LargeUtf8, Utf8)`.
                     // TODO: Native support Utf8View for regexp_match.
                     Exact(vec![Utf8, Utf8]),
-                    Exact(vec![LargeUtf8, Utf8]),
+                    Exact(vec![LargeUtf8, LargeUtf8]),
                     Exact(vec![Utf8, Utf8, Utf8]),
-                    Exact(vec![LargeUtf8, Utf8, Utf8]),
+                    Exact(vec![LargeUtf8, LargeUtf8, LargeUtf8]),
                 ],
                 Volatility::Immutable,
             ),
@@ -131,7 +131,7 @@ pub fn regexp_match<T: OffsetSizeTrait>(args: &[ArrayRef]) -> Result<ArrayRef> {
             let flags = as_generic_string_array::<T>(&args[2])?;
 
             if flags.iter().any(|s| s == Some("g")) {
-                return plan_err!("regexp_match() does not support the \"global\" option")
+                return plan_err!("regexp_match() does not support the \"global\" option");
             }
 
             regexp::regexp_match(values, regex, Some(flags))
diff --git a/datafusion/sqllogictest/test_files/string/dictionary_utf8.slt b/datafusion/sqllogictest/test_files/string/dictionary_utf8.slt
index ea3c9b8eb6ca..c181f613ee9a 100644
--- a/datafusion/sqllogictest/test_files/string/dictionary_utf8.slt
+++ b/datafusion/sqllogictest/test_files/string/dictionary_utf8.slt
@@ -53,36 +53,6 @@ Xiangpeng datafusion数据融合 false true false true
 Raphael datafusionДатаФусион false false false false
 NULL NULL NULL NULL NULL NULL
 
-# TODO: move it back to `string_query.slt.part` after fixing the issue
-# see detail: https://github.com/apache/datafusion/issues/12664
-query BBBB
-SELECT
-  REGEXP_LIKE(ascii_1, 'an'),
-  REGEXP_LIKE(unicode_1, 'таФ'),
-  REGEXP_LIKE(ascii_1, NULL),
-  REGEXP_LIKE(unicode_1, NULL)
-FROM test_basic_operator;
-----
-false false NULL NULL
-true false NULL NULL
-false true NULL NULL
-NULL NULL NULL NULL
-
-# TODO: move it back to `string_query.slt.part` after fixing the issue
-# see detail: https://github.com/apache/datafusion/issues/12664
-query ????
-SELECT
-  REGEXP_MATCH(ascii_1, 'an'),
-  REGEXP_MATCH(unicode_1, 'таФ'),
-  REGEXP_MATCH(ascii_1, NULL),
-  REGEXP_MATCH(unicode_1, NULL)
-FROM test_basic_operator;
-----
-NULL NULL NULL NULL
-[an] NULL NULL NULL
-NULL [таФ] NULL NULL
-NULL NULL NULL NULL
-
 #
 # common test for string-like functions and operators
 #
diff --git a/datafusion/sqllogictest/test_files/string/string.slt b/datafusion/sqllogictest/test_files/string/string.slt
index 6b89147c5c4f..f4e83966f78f 100644
--- a/datafusion/sqllogictest/test_files/string/string.slt
+++ b/datafusion/sqllogictest/test_files/string/string.slt
@@ -63,36 +63,6 @@ Xiangpeng datafusion数据融合 false true false true
 Raphael datafusionДатаФусион false false false false
 NULL NULL NULL NULL NULL NULL
 
-# TODO: move it back to `string_query.slt.part` after fixing the issue
-# see detail: https://github.com/apache/datafusion/issues/12664
-query BBBB
-SELECT
-  REGEXP_LIKE(ascii_1, 'an'),
-  REGEXP_LIKE(unicode_1, 'таФ'),
-  REGEXP_LIKE(ascii_1, NULL),
-  REGEXP_LIKE(unicode_1, NULL)
-FROM test_basic_operator;
-----
-false false NULL NULL
-true false NULL NULL
-false true NULL NULL
-NULL NULL NULL NULL
-
-# TODO: move it back to `string_query.slt.part` after fixing the issue
-# see detail: https://github.com/apache/datafusion/issues/12664
-query ????
-SELECT
-  REGEXP_MATCH(ascii_1, 'an'),
-  REGEXP_MATCH(unicode_1, 'таФ'),
-  REGEXP_MATCH(ascii_1, NULL),
-  REGEXP_MATCH(unicode_1, NULL)
-FROM test_basic_operator;
-----
-NULL NULL NULL NULL
-[an] NULL NULL NULL
-NULL [таФ] NULL NULL
-NULL NULL NULL NULL
-
 # TODO: move it back to `string_query.slt.part` after fixing the issue
 # see detail: https://github.com/apache/datafusion/issues/12670
 query IIIIII
diff --git a/datafusion/sqllogictest/test_files/string/string_query.slt.part b/datafusion/sqllogictest/test_files/string/string_query.slt.part
index 0af0a6a642b2..3ba2b31bbab2 100644
--- a/datafusion/sqllogictest/test_files/string/string_query.slt.part
+++ b/datafusion/sqllogictest/test_files/string/string_query.slt.part
@@ -856,39 +856,47 @@ NULL NULL
 # Test REGEXP_LIKE
 # --------------------------------------
 
-# TODO: LargeString does not support REGEXP_LIKE. Enable this after fixing the issue
-# see issue: https://github.com/apache/datafusion/issues/12664
-#query BBBB
-#SELECT
-#  REGEXP_LIKE(ascii_1, 'an'),
-#  REGEXP_LIKE(unicode_1, 'таФ'),
-#  REGEXP_LIKE(ascii_1, NULL),
-#  REGEXP_LIKE(unicode_1, NULL)
-#FROM test_basic_operator;
-#----
-#false false NULL NULL
-#true false NULL NULL
-#false true NULL NULL
-#NULL NULL NULL NULL
+query BBBBBBBB
+SELECT
+  -- without flags
+  REGEXP_LIKE(ascii_1, 'an'),
+  REGEXP_LIKE(unicode_1, 'таФ'),
+  REGEXP_LIKE(ascii_1, NULL),
+  REGEXP_LIKE(unicode_1, NULL),
+  -- with flags
+  REGEXP_LIKE(ascii_1, 'AN', 'i'),
+  REGEXP_LIKE(unicode_1, 'ТаФ', 'i'),
+  REGEXP_LIKE(ascii_1, NULL, 'i'),
+  REGEXP_LIKE(unicode_1, NULL, 'i')
+  FROM test_basic_operator;
+----
+false false NULL NULL true false NULL NULL
+true false NULL NULL true false NULL NULL
+false true NULL NULL false true NULL NULL
+NULL NULL NULL NULL NULL NULL NULL NULL
 
 # --------------------------------------
 # Test REGEXP_MATCH
 # --------------------------------------
 
-# TODO: LargeString does not support REGEXP_MATCH. Enable this after fixing the issue
-# see issue: https://github.com/apache/datafusion/issues/12664
-#query ????
-#SELECT
-#  REGEXP_MATCH(ascii_1, 'an'),
-#  REGEXP_MATCH(unicode_1, 'таФ'),
-#  REGEXP_MATCH(ascii_1, NULL),
-#  REGEXP_MATCH(unicode_1, NULL)
-#FROM test_basic_operator;
-#----
-#NULL NULL NULL NULL
-#[an] NULL NULL NULL
-#NULL [таФ] NULL NULL
-#NULL NULL NULL NULL
+query ????????
+SELECT
+  -- without flags
+  REGEXP_MATCH(ascii_1, 'an'),
+  REGEXP_MATCH(unicode_1, 'ТаФ'),
+  REGEXP_MATCH(ascii_1, NULL),
+  REGEXP_MATCH(unicode_1, NULL),
+  -- with flags
+  REGEXP_MATCH(ascii_1, 'AN', 'i'),
+  REGEXP_MATCH(unicode_1, 'таФ', 'i'),
+  REGEXP_MATCH(ascii_1, NULL, 'i'),
+  REGEXP_MATCH(unicode_1, NULL, 'i')
+FROM test_basic_operator;
+----
+NULL NULL NULL NULL [An] NULL NULL NULL
+[an] NULL NULL NULL [an] NULL NULL NULL
+NULL NULL NULL NULL NULL [таФ] NULL NULL
+NULL NULL NULL NULL NULL NULL NULL NULL
 
 # --------------------------------------
 # Test REPEAT
diff --git a/datafusion/sqllogictest/test_files/string/string_view.slt b/datafusion/sqllogictest/test_files/string/string_view.slt
index fb82726e3a9d..4e7857ad804b 100644
--- a/datafusion/sqllogictest/test_files/string/string_view.slt
+++ b/datafusion/sqllogictest/test_files/string/string_view.slt
@@ -50,36 +50,6 @@ false false
 false true
 NULL NULL
 
-# TODO: move it back to `string_query.slt.part` after fixing the issue
-# see detail: https://github.com/apache/datafusion/issues/12664
-query BBBB
-SELECT
-  REGEXP_LIKE(ascii_1, 'an'),
-  REGEXP_LIKE(unicode_1, 'таФ'),
-  REGEXP_LIKE(ascii_1, NULL),
-  REGEXP_LIKE(unicode_1, NULL)
-FROM test_basic_operator;
-----
-false false NULL NULL
-true false NULL NULL
-false true NULL NULL
-NULL NULL NULL NULL
-
-# TODO: move it back to `string_query.slt.part` after fixing the issue
-# see detail: https://github.com/apache/datafusion/issues/12664
-query ????
-SELECT
-  REGEXP_MATCH(ascii_1, 'an'),
-  REGEXP_MATCH(unicode_1, 'таФ'),
-  REGEXP_MATCH(ascii_1, NULL),
-  REGEXP_MATCH(unicode_1, NULL)
-FROM test_basic_operator;
-----
-NULL NULL NULL NULL
-[an] NULL NULL NULL
-NULL [таФ] NULL NULL
-NULL NULL NULL NULL
-
 # TODO: move it back to `string_query.slt.part` after fixing the issue
 # see detail: https://github.com/apache/datafusion/issues/12670
 query IIIIII