This works for me (I edited my code a little to show):

    // First log in
    $url = 'http://[your-domain]/rest/V1/integration/admin/token';
    $body = '{"username":"user", "password":"pass"}';
    $header = 'Content-type: application/json';
    $options = [    'method' => 'POST',
    				'content' => $body,
    				'header' => $header
    		   ];
    $context = stream_context_create(['http' => $options]);
    $token = json_decode(file_get_contents($url, false, $context));
    
    // Some settings
    
    $header = 'Authorization: Bearer ' . $token . "\r\n"
    	. 'Content-type: application/json';
    $options = [    'method' => 'GET',
    				'content' => $body,
    				'header' => $header
    		   ];
    $context = stream_context_create(['http' => $options]);
    
    $url = 'http://outpro.lt/index.php/rest/V1/orders/'
    	. '?searchCriteria[filter_groups][0][filters][0][field]=status&searchCriteria[filter_groups][0][filters][0][value]=pending'
    	//. '&searchCriteria[sortOrders][0][field]=increment_id' // To sort Desc
    	. '&fields=items[increment_id,entity_id]';
    
    //print file_get_contents($url, false, $context) . "\n"; // Check full json if you want
    
    // Generate json output
    $json_contents = file_get_contents($url, false, $context) . "\n";
    $order = json_decode($json_contents);
    $answer = '{';
    if ($order->items) { 
    	foreach($order->items as $key => $value) {
    		$answer .= '"'. $value->entity_id . '":"' . $value->increment_id . '",';
    	}
    	$answer = substr($answer,0,strlen($answer)-1);
    	$answer .= '}';
    	echo $answer;
    }