Barack Obama has more than 17 million followers on Twitter.
Obama was the first head of state to sign up on the social media service and the PR firm said he sent the most popular tweet of any world leader, which read: "Same-sex couples should be able to get married." His popularity ranks him fifth in the entire Twitterverse, just behind @britneyspears, according to the study.
But only 1 percent of the tweets from Obama's account are replies, putting him way down the world leader rankings in terms of engaging with his army of followers.
For a real conversation, try an African leader like Uganda's @AmamaMbabazi or Rwanda's @PaulKagame, whose tweets are more than 90 percent replies, the PR firm said. Or Venezuela's Hugo Chavez, the second most popular leader on Twitter, who tweets as @chavezcandanga and replies in 38 percent of his messages.
Ninety-nine world leaders and governments have never sent a single reply, according to the Burson-Marsteller study.
Obama ranks near the bottom of the survey in terms of connections with other leaders, although he beats Russian President Vladimir Putin, who is not following any of his peers on Twitter.
The study said Obama is mutually following only two leaders: Norwegian Prime Minister Jens Stoltenberg and Russian President Dmitry Medvedev, who was one of only three presidents to have tweeted an obscenity. The Kremlin blamed the lapse on an unidentified official who had interfered with the feed and it was deleted.
Another was Panama's Ricardo Martinelli, whose reference to "HP" was taken to refer to the Spanish for "son of a bitch." He later deleted the tweet and said it meant "Harry Potter."
The only presidential obscenity still visible is by Estonian President Toomas Ilves, who struck back at criticism by economist Paul Krugman with the tweet: "Let's sh *t on East Europeans: their English is bad, won't respond & actually do what they've agreed to & reelect govts that are responsible."
Like many government accounts, the vast majority of Obama's messages were sent on his behalf by web-savvy assistants.
Only eight of almost 5,000 tweets sent from the @BarackObama account were personally signed off with his initials "-BO," including a Valentine's Day message to his wife.
Does Twitter diplomacy work?
According to a new study, almost two-thirds of world leaders have joined Twitterverse where President Barack Obama and his tweet on gay marriage are the most popular to date. But the rise in so-called 'Twiplomacy' resembles something of an echo chamber, where about a third of them don't follow each other and dozens of them don't even follow any other Twitterers.