The controversial articles force journalists to reveal their sources and make defamation a criminal offence.
Parliament approved the code in April, and President Atifete Jahjaga rejected it and returned it to parliament for a second vote.
But lawmakers voted on July 22 in favour of keeping both articles.
Prime Minister Hashim Thaci said he would send the code back for a third vote, without the disputed articles.
Kosovo has faced steady criticism from international bodies for not doing enough to protect journalists and the freedom of the press.
The EU representative in Kosovo said he was disappointed with parliament's decision.