Conversations will now be shown together rather than in a reverse chronological order, in a feature which has already rolled out to some handsets and will now be updated in all iPhone and Android apps, as well as twitter.com.
Up to three tweets will be displayed in a sequence, with a line connecting them to show they are part of the same conversation. If users want to view the whole conversation they can tap on the first tweet.
In a statement on Thursday, the company said: "From buzz about the VMAs to debates around upcoming football games, people come to Twitter to take part in these real-time, global, public conversations.
"To date, such exchanges haven't always been easy to follow. With this in mind, we've now made it easier for you to see conversations as they're taking place."
Some commentators have suggested the move will make the social networking site more like Facebook, with tweets becoming more like comments on a status posting.
It is hoped that easier to follow conversations will make users stay longer on the site, becoming involved in more conversations.
The company also announced a function that would make it possible to share Twitter conversations via email, even with friends who do not have a presence on a site.
Twitter also said it said it would be introducing a 'report tweet' button for abusive messages, following a campaign by a number of women who were targeted on the site.