International Court of Justice (ICJ) president Hisashi Owada was among three judges reelected to nine-year terms in votes at the 15 member UN Security Council and 193 country General Assembly.
Slovakia's Peter Tomka and China's Xue Hanqin were also re-elected. Giorgio Gaja of Italy is the first newcomer to the panel of 15 judges who sit in The Hague.
But five rounds of voting at the two chambers failed to get an absolute ajority behind either Julia Sebutinde of Uganda or El Hadji Mansour Tall of Senegal. The election was suspended to a later date.
Established in 1945, the ICJ settles legal disputes between states and gives advisory opinions on legal questions referred to it by UN agencies and departments.
Owada said in his annual report to the UN General Assembly in late October that there has been a "remarkable increase in the number of cases" which meant many judges had to sit in parallel hearings.
He said there had never been less than 15 cases at any one time during his three year presidency, and there had been up to 28.
Speaking after his election, Gaja also highlighted the greater workload which he called a good sign.
"Twenty years ago the situation was quite different and one had to wonder what the significance was of the court because of the few cases brought," Gaja told reporters.