diff --git a/src/wp-includes/html-api/class-wp-html-open-elements.php b/src/wp-includes/html-api/class-wp-html-open-elements.php
index 5ce1f8feb552c..cb913853f0ee9 100644
--- a/src/wp-includes/html-api/class-wp-html-open-elements.php
+++ b/src/wp-includes/html-api/class-wp-html-open-elements.php
@@ -530,31 +530,31 @@ public function pop(): bool {
 	}
 
 	/**
-	 * Pops nodes off of the stack of open elements until one with the given tag name has been popped.
+	 * Pops nodes off of the stack of open elements until an HTML tag with the given name has been popped.
 	 *
 	 * @since 6.4.0
 	 *
 	 * @see WP_HTML_Open_Elements::pop
 	 *
-	 * @param string $tag_name Name of tag that needs to be popped off of the stack of open elements.
+	 * @param string $html_tag_name Name of tag that needs to be popped off of the stack of open elements.
 	 * @return bool Whether a tag of the given name was found and popped off of the stack of open elements.
 	 */
-	public function pop_until( string $tag_name ): bool {
+	public function pop_until( string $html_tag_name ): bool {
 		foreach ( $this->walk_up() as $item ) {
-			if ( 'context-node' === $item->bookmark_name ) {
-				return true;
-			}
-
 			$this->pop();
 
+			if ( 'html' !== $item->namespace ) {
+				continue;
+			}
+
 			if (
-				'(internal: H1 through H6 - do not use)' === $tag_name &&
+				'(internal: H1 through H6 - do not use)' === $html_tag_name &&
 				in_array( $item->node_name, array( 'H1', 'H2', 'H3', 'H4', 'H5', 'H6' ), true )
 			) {
 				return true;
 			}
 
-			if ( $tag_name === $item->node_name ) {
+			if ( $html_tag_name === $item->node_name ) {
 				return true;
 			}
 		}
diff --git a/src/wp-includes/html-api/class-wp-html-processor.php b/src/wp-includes/html-api/class-wp-html-processor.php
index 55b906136820f..cb581fac3988f 100644
--- a/src/wp-includes/html-api/class-wp-html-processor.php
+++ b/src/wp-includes/html-api/class-wp-html-processor.php
@@ -5428,6 +5428,11 @@ private function reset_insertion_mode_appropriately(): void {
 				}
 			}
 
+			// All of the following rules are for matching HTML elements.
+			if ( 'html' !== $node->namespace ) {
+				continue;
+			}
+
 			switch ( $node->node_name ) {
 				/*
 				 * > 4. If node is a `select` element, run these substeps:
@@ -5443,6 +5448,10 @@ private function reset_insertion_mode_appropriately(): void {
 				case 'SELECT':
 					if ( ! $last ) {
 						foreach ( $this->state->stack_of_open_elements->walk_up( $node ) as $ancestor ) {
+							if ( 'html' !== $ancestor->namespace ) {
+								continue;
+							}
+
 							switch ( $ancestor->node_name ) {
 								/*
 								 * > 5. If _ancestor_ is a `template` node, jump to the step below
diff --git a/tests/phpunit/tests/html-api/wpHtmlProcessor.php b/tests/phpunit/tests/html-api/wpHtmlProcessor.php
index e9b9063f77a7b..17dd2ff7fbd68 100644
--- a/tests/phpunit/tests/html-api/wpHtmlProcessor.php
+++ b/tests/phpunit/tests/html-api/wpHtmlProcessor.php
@@ -520,6 +520,30 @@ public function test_foreign_content_script_self_closing() {
 		$this->assertTrue( $processor->next_tag( 'script' ) );
 	}
 
+	/**
+	 * Ensures that the HTML Processor correctly handles TEMPLATE tag closing and namespaces.
+	 *
+	 * This is a tricky test case that corresponds to the html5lib tests "template/line1466".
+	 *
+	 * When the `</template>` token is reached it is in the HTML namespace (thanks to the
+	 * SVG `foreignObject` element). It is not handled as foreign content; therefore, it
+	 * closes the open HTML `TEMPLATE` element (the first `<template>` token) - _not_ the
+	 * SVG `TEMPLATE` element (the second `<template>` token).
+	 *
+	 * The test is included here because it may show up as unsupported markup and be skipped by
+	 * the html5lib test suite.
+	 *
+	 * @ticket 61576
+	 */
+	public function test_template_tag_closes_html_template_element() {
+		$processor = WP_HTML_Processor::create_fragment( '<template><svg><template><foreignObject><div></template><div>' );
+
+		$this->assertTrue( $processor->next_tag( 'DIV' ) );
+		$this->assertSame( array( 'HTML', 'BODY', 'TEMPLATE', 'SVG', 'TEMPLATE', 'FOREIGNOBJECT', 'DIV' ), $processor->get_breadcrumbs() );
+		$this->assertTrue( $processor->next_tag( 'DIV' ) );
+		$this->assertSame( array( 'HTML', 'BODY', 'DIV' ), $processor->get_breadcrumbs() );
+	}
+
 	/**
 	 * Ensures that the tag processor is case sensitive when removing CSS classes in no-quirks mode.
 	 *