In Singapore's case, Parliament would have to pass a Bill before Singapore can ratify the convention.
Of the 70 countries which sent representatives to the Singapore Convention Signing Ceremony and Conference, held at the Shangri-La Hotel, 46 signed the international mediation treaty.
"Given that the UN passed its resolution in December of last year, we are talking about.. seven, eight months. It's quite unprecedented in terms of numbers for the signing ceremony," Mr Shanmugam said.
He noted that the signatories include the world's two largest economies, the United States and China, and three of the four largest economies in Asia - China, India and South Korea.
Mr Shanmugam said that the convention signing ceremony is one of five significant events taking place in Singapore that relate to the legal sector.
On Monday, Insol, a London-based umbrella body for restructuring and insolvency associations,
launched its Asian arm in Singapore
. On Thursday, Singapore will open the revamped Maxwell Chambers, and on the same day, the American Arbitration Association's International Center for Dispute Resolution will also set up its Asian hub here.
This week, the International Bar Association also held a conference on arbitration in Singapore, Mr Shanmugam noted.