The 193 members of the UN General Assembly and 15 of the Security Council will reconvene on Monday to decide between Bhandari, 70, and Greenwood, 62.
Based in The Hague, the International Court of Justice (ICJ) has a bench of 15 judges, five of whom are elected every three years for a nine-year term.
Established in 1945, the role of the ICJ is to settle, in accordance with international law, legal disputes submitted to it by states and to give advisory opinions on legal questions.
Nawaf Salam of Lebanon was also in the fray, making a total of six candidate for five positions.
More From This Section
Judges of France, Somalia, Lebanon and Brazil were elected after fourth round of voting late in the afternoon, as they received absolute majority in both the General Assembly and the Security Council elections.
Stakes are now high for both India and Britain for the last seat.
However, in the 15-member Security Council Greenwood got majority (nine) of the votes as against six votes by Bhandari.
As a result, another round of votes has been scheduled for Monday.
As per the United Nation's ICJ election rules, candidates need to get absolute majority in both the General Assembly and the Security Council. Both elections are held simultaneously but independently of each other.
That means 97 votes in the Assembly and eight votes in the Security Council are required to win the ICJ election.
A former judge of the Supreme Court, Bhandari was elected to the International Court of Justice in April 27, 2012 following a vacancy after the resignation of sitting court judge Awn Shawkat Al-Khasawneh from Jordon on being appointed as the Prime Minister.
Bhandari had received 122 votes in the UN General assembly as against 58 for Florentino Feliciano from the Philippines.
The ICJ, on India's petition in May, stayed the execution of Indian national and former naval officer Kulbhushan Jadhav who was sentenced to death by a Pakistan military court on the charge of "spying".