diff --git a/src/wp-includes/query.php b/src/wp-includes/query.php
index fa59b0f55f..23c5d7637f 100644
--- a/src/wp-includes/query.php
+++ b/src/wp-includes/query.php
@@ -3123,11 +3123,12 @@ class WP_Query {
 			if ( !$page )
 				$page = 1;
 
-			if ( empty($q['offset']) ) {
-				$pgstrt = absint( ( $page - 1 ) * $q['posts_per_page'] ) . ', ';
-			} else { // we're ignoring $page and using 'offset'
-				$q['offset'] = absint($q['offset']);
+			// If 'offset' is provided, it takes precedence over 'paged'.
+			if ( isset( $q['offset'] ) && is_numeric( $q['offset'] ) ) {
+				$q['offset'] = absint( $q['offset'] );
 				$pgstrt = $q['offset'] . ', ';
+			} else {
+				$pgstrt = absint( ( $page - 1 ) * $q['posts_per_page'] ) . ', ';
 			}
 			$limits = 'LIMIT ' . $pgstrt . $q['posts_per_page'];
 		}
diff --git a/tests/phpunit/tests/query.php b/tests/phpunit/tests/query.php
index 4bbf882d65..a7c20a9d2b 100644
--- a/tests/phpunit/tests/query.php
+++ b/tests/phpunit/tests/query.php
@@ -459,4 +459,42 @@ class Tests_Query extends WP_UnitTestCase {
 	public function filter_parse_query_to_modify_queried_post_id( $query ) {
 		$post = get_queried_object();
 	}
+
+	/**
+	 * @ticket 34060
+	 */
+	public function test_offset_0_should_override_page() {
+		$q = new WP_Query( array(
+			'paged' => 2,
+			'posts_per_page' => 5,
+			'offset' => 0,
+		) );
+
+		$this->assertContains( 'LIMIT 0, 5', $q->request );
+	}
+
+	/**
+	 * @ticket 34060
+	 */
+	public function test_offset_should_be_ignored_when_not_set() {
+		$q = new WP_Query( array(
+			'paged' => 2,
+			'posts_per_page' => 5,
+		) );
+
+		$this->assertContains( 'LIMIT 5, 5', $q->request );
+	}
+
+	/**
+	 * @ticket 34060
+	 */
+	public function test_offset_should_be_ignored_when_passed_a_non_numeric_value() {
+		$q = new WP_Query( array(
+			'paged' => 2,
+			'posts_per_page' => 5,
+			'offset' => '',
+		) );
+
+		$this->assertContains( 'LIMIT 5, 5', $q->request );
+	}
 }