How to parse string pairs over multiple lines?

I'd like to parse content like:

tag = value
tag2 = value2
tag3 = value3

with the relaxation of allowing values over multiple lines and disregarding comments of the next tag. A tag is identified by not starting with the comment identifier '#' and starting at a new line. So this:

tag = value
  value continuation
tag2 = value2
  value continuation2
# comment for tag3
tag3 = value3

should parse the mapping:

tag : "value\nvalue continuation"
tag2 : "value2\nvalue continuation2"
tag3 : "value3"

How can I achieve this in a clean way? My current code for parsing one-line pairs looks sth like this:

while( std::getline( istr, line ) )
{
  ++lineCount;
  if( line[0] == '#' )
    currentComment.push_back( line );
  else if( isspace( line[0]) || line[0] == '\0' )
    currentComment.clear( );
  else
  {
    auto tag = Utils::string::splitString( line, '=' );
    if( tag.size() != 2 || line[line.size() - 1] == '=')
    {
      std::cerr << "Wrong tag syntax in line #" << lineCount << std::endl;
      return nullptr;
    }
    tagLines.push_back( line );
    currentComment.clear( );
  } 
}

Note that I don't require the results being stored in the types of containers that are currently used. I can switch to anything that fits better unless I get sets of (comment, tagname, value).