STRASBOURG, Oct 5 (Reuters) - U.S. tech giants such as Apple (AAPL.O), Google, Facebook (FB.O) and Amazon (AMZN.O) should be regulated by the EU country where they are based under proposed EU rules, a top lawmaker said on Tuesday, knocking back efforts by some countries to broaden the planned act"s scope. The country of origin principle is set out in EU antitrust chief Margrethe Vestager"s draft rules known as the Digital Services Act which requires U.S. tech giants to do more to police the internet for illegal and harmful content. The principle means Ireland is responsible for regulating Apple, Alphabet (GOOGL.O) unit Google and Facebook because they have their European headquarters there while Amazon is subject to Luxembourg"s supervision. France and a few other countries are seeking to broaden the scope, worried that enforcement concentrated in just two countries may weaken the rules and also slow down decision-making. Lawmaker Christel Schaldemose, who is steering the DSA through the European Parliament and has power to amend or add other provisions to it, supports the act"s core proposal. "It makes sense to keep the country of origin principle," she told Reuters in an interview. Schaldemose however wants to go one step further than Vestager by including a ban on some targeted advertising in the DSA. "Targeted advertisements that are based on your behaviour on Facebook, for instance, that should not be allowed. Advertisements based on the fact that you have visited websites for buying shoes and things like that, classic commercial advertisements should probably be allowed," she said.Schaldemoe said she hopes to finalise her draft with other lawmakers in the next two months so she can thrash out a deal with EU countries next year before the proposed rules can be implemented.