diff --git a/src/wp-includes/embed.php b/src/wp-includes/embed.php
index 3fb8968c7c62c..b53c00f67ddc7 100644
--- a/src/wp-includes/embed.php
+++ b/src/wp-includes/embed.php
@@ -1233,11 +1233,23 @@ function print_embed_sharing_dialog() {
  * @since 4.5.0
  */
 function the_embed_site_title() {
+	$site_icon_url = get_site_icon_url( 32, includes_url( 'images/w-logo-blue.png' ) );
+
+	$icon_img = '';
+	if ( $site_icon_url ) {
+		$site_icon_url_2x = get_site_icon_url( 64, includes_url( 'images/w-logo-blue.png' ) );
+		$srcset           = ( $site_icon_url_2x && $site_icon_url !== $site_icon_url_2x ) ? sprintf( ' srcset="%s 2x"', esc_url( $site_icon_url_2x ) ) : '';
+		$icon_img         = sprintf(
+			'<img src="%s"%s width="32" height="32" alt="" class="wp-embed-site-icon" />',
+			esc_url( $site_icon_url ),
+			$srcset
+		);
+	}
+
 	$site_title = sprintf(
-		'<a href="%s" target="_top"><img src="%s" srcset="%s 2x" width="32" height="32" alt="" class="wp-embed-site-icon" /><span>%s</span></a>',
+		'<a href="%s" target="_top">%s<span>%s</span></a>',
 		esc_url( home_url() ),
-		esc_url( get_site_icon_url( 32, includes_url( 'images/w-logo-blue.png' ) ) ),
-		esc_url( get_site_icon_url( 64, includes_url( 'images/w-logo-blue.png' ) ) ),
+		$icon_img,
 		esc_html( get_bloginfo( 'name' ) )
 	);
 
diff --git a/src/wp-includes/general-template.php b/src/wp-includes/general-template.php
index 47e2aeb2ebb05..1ba2912953ae8 100644
--- a/src/wp-includes/general-template.php
+++ b/src/wp-includes/general-template.php
@@ -978,7 +978,10 @@ function get_site_icon_url( $size = 512, $url = '', $blog_id = 0 ) {
 		} else {
 			$size_data = array( $size, $size );
 		}
-		$url = wp_get_attachment_image_url( $site_icon_id, $size_data );
+		$attachment_url = wp_get_attachment_image_url( $site_icon_id, $size_data );
+		if ( $attachment_url ) {
+			$url = $attachment_url;
+		}
 	}
 
 	if ( $switched_blog ) {
diff --git a/tests/phpunit/tests/general/template.php b/tests/phpunit/tests/general/template.php
index d3b35a2c46c2b..23c689466c162 100644
--- a/tests/phpunit/tests/general/template.php
+++ b/tests/phpunit/tests/general/template.php
@@ -122,6 +122,27 @@ public function test_get_site_icon_url() {
 		$this->assertEmpty( get_site_icon_url(), 'Site icon URL should not be set after removal.' );
 	}
 
+	/**
+	 * @ticket 65098
+	 * @group site_icon
+	 * @covers ::get_site_icon_url
+	 * @requires function imagejpeg
+	 */
+	public function test_get_site_icon_url_returns_fallback_when_attachment_url_fails() {
+		$this->set_site_icon();
+
+		$fallback = 'https://example.com/fallback-icon.png';
+		add_filter( 'wp_get_attachment_image_src', '__return_false' );
+
+		try {
+			$url = get_site_icon_url( 32, $fallback );
+		} finally {
+			remove_filter( 'wp_get_attachment_image_src', '__return_false' );
+		}
+
+		$this->assertSame( $fallback, $url, 'Fallback URL should be returned when attachment URL lookup fails.' );
+	}
+
 	/**
 	 * @group site_icon
 	 * @covers ::site_icon_url
@@ -807,4 +828,116 @@ public function test_get_the_archive_title_is_correct_for_author_queries() {
 		$this->assertSame( $user_with_posts->display_name, $title_when_posts );
 		$this->assertSame( $user_with_no_posts->display_name, $title_when_no_posts );
 	}
+
+	/**
+	 * @ticket 65098
+	 * @group site_icon
+	 * @covers ::the_embed_site_title
+	 * @requires function imagejpeg
+	 */
+	public function test_the_embed_site_title_contains_site_icon_when_set() {
+		$this->set_site_icon();
+
+		$url_32 = get_site_icon_url( 32 );
+		$url_64 = get_site_icon_url( 64 );
+
+		ob_start();
+		the_embed_site_title();
+		$output = ob_get_clean();
+
+		$this->assertStringContainsString( 'wp-embed-site-icon', $output, 'Output should contain site icon img tag.' );
+		$this->assertStringContainsString( esc_url( $url_32 ), $output, 'Output should contain 32px site icon URL.' );
+		$this->assertStringContainsString( esc_url( $url_64 ), $output, 'Output should contain 64px site icon URL in srcset.' );
+	}
+
+	/**
+	 * @ticket 65098
+	 * @group site_icon
+	 * @covers ::the_embed_site_title
+	 * @requires function imagejpeg
+	 */
+	public function test_the_embed_site_title_uses_fallback_when_attachment_url_fails() {
+		$this->set_site_icon();
+
+		// Simulate wp_get_attachment_image_url() failing.
+		add_filter( 'wp_get_attachment_image_src', '__return_false' );
+
+		try {
+			ob_start();
+			the_embed_site_title();
+			$output = ob_get_clean();
+		} finally {
+			remove_filter( 'wp_get_attachment_image_src', '__return_false' );
+		}
+
+		$fallback = includes_url( 'images/w-logo-blue.png' );
+		$this->assertStringContainsString( 'wp-embed-site-icon', $output, 'Output should contain site icon img tag with fallback.' );
+		$this->assertStringContainsString( esc_url( $fallback ), $output, 'Output should contain fallback URL when attachment URL fails.' );
+		$this->assertStringNotContainsString( 'src=""', $output, 'Output should not contain empty src attribute.' );
+	}
+
+	/**
+	 * @ticket 65098
+	 * @group site_icon
+	 * @covers ::the_embed_site_title
+	 */
+	public function test_the_embed_site_title_omits_img_when_url_is_empty() {
+		// Force get_site_icon_url() to return empty string via filter.
+		add_filter( 'get_site_icon_url', '__return_empty_string' );
+
+		try {
+			ob_start();
+			the_embed_site_title();
+			$output = ob_get_clean();
+		} finally {
+			remove_filter( 'get_site_icon_url', '__return_empty_string' );
+		}
+
+		$this->assertStringNotContainsString( 'wp-embed-site-icon', $output, 'img tag should be omitted when URL is empty.' );
+		$this->assertStringNotContainsString( 'src=""', $output, 'Output should not contain empty src attribute.' );
+		$this->assertStringContainsString( get_bloginfo( 'name' ), $output, 'Site name should still be present.' );
+	}
+
+	/**
+	 * @ticket 65098
+	 * @group site_icon
+	 * @covers ::the_embed_site_title
+	 */
+	public function test_the_embed_site_title_omits_srcset_when_1x_and_2x_urls_are_identical() {
+		// Force both sizes to return the same URL.
+		$svg_url = 'https://example.com/icon.svg';
+		$filter  = static function () use ( $svg_url ) {
+			return $svg_url;
+		};
+
+		add_filter( 'get_site_icon_url', $filter );
+
+		try {
+			ob_start();
+			the_embed_site_title();
+			$output = ob_get_clean();
+		} finally {
+			remove_filter( 'get_site_icon_url', $filter );
+		}
+
+		$this->assertStringNotContainsString( 'srcset=', $output, 'srcset should be omitted when 1x and 2x URLs are identical.' );
+		$this->assertStringContainsString( esc_url( $svg_url ), $output, '1x URL should still be present in src.' );
+	}
+
+	/**
+	 * @ticket 65098
+	 * @group site_icon
+	 * @covers ::the_embed_site_title
+	 */
+	public function test_the_embed_site_title_uses_fallback_without_srcset_when_no_site_icon_set() {
+		ob_start();
+		the_embed_site_title();
+		$output = ob_get_clean();
+
+		$fallback = includes_url( 'images/w-logo-blue.png' );
+
+		$this->assertStringContainsString( 'wp-embed-site-icon', $output, 'Fallback icon img should be present when no site icon is set.' );
+		$this->assertStringContainsString( esc_url( $fallback ), $output, 'Output should contain fallback icon URL.' );
+		$this->assertStringNotContainsString( 'srcset=', $output, 'srcset should be omitted when 1x and 2x fallback URLs are identical.' );
+	}
 }