"We have expressed our concern that Twitter and other social media companies can not be used as a platform for accelerating hate, disinformation or discrimination... We are watching the situation very closely," Dujarric told a briefing.
The UN has not had any specific contacts with Twitter, he added.
The United Nations is a big user of Twitter - having dozens of accounts for all its departments, officials and parts of the UN. The main UN account has over 16 million users.
On Thursday, Musk closed the $44 billion deal to acquire Twitter, negotiations for which began in April. The acquisition was delayed due to concerns by Musk about the number of fake accounts on the platform. The billionaire plans to liberalize the social network's editorial policy, which has been widely criticized for heavily censoring content.
On Friday, the media reported that Twitter had already begun laying off employees. The Washington Post, citing corporate documents, reported earlier that Musk intended to fire 75% of Twitter workers. At the same time, the entrepreneur denied these reports.