Amid heavy security, Britain's Queen Elizabeth II opened the three-day-long summit of the bloc, having a geographic spread covering six continents with a total population of over 2.2 billion people.
India, the largest member of the grouping, is being represented by External Affairs Minister Sushma Swaraj while other leaders attending it included Pakistan Prime Minister Nawaz Sharif, Australian Prime Minister Malcolm Turnbull, Sri Lankan President Maithripala Sirisena, UK Prime MinisterDavid Cameron and Canadian Prime Minister Justin Trudea.
In her inaugural address, Queen Elizabeth elaborated accomplishments of the Commonwealth and particularly delved on initiatives by the grouping in saving the world's forests.
In his welcome address, Prime Minister of Malta Joseph Muscatsaid combating terrorism and extremism should be the top most priority of Commonwealth and sought wider discussion among the member countries to deal with the challenge of climate change.
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"We live in a time when young people within our Commonwealth are attracted to join terrorist groups. This should be part of our immediate fight," he said.
"The Commonwealth has a vital role to play in broadening international efforts to counter extremism. Its civil society and education networks make it particularly well-placed to complement international efforts to build counter narratives to this poisonous extremist ideology," Cameron said.
"This is the struggle of our generation, but by working together we will defeat this extremism scourge that is a threat to us all."
The summit is scheduled to be addressed by UN Secretary
General Ban Ki-moon and French President Francois Hollande.
The summit is also likely to deliberate on issues relating to trade and commerce and migration among others.
The Commonwealth includes some of the world's largest, smallest, richest and poorest countries.
Thirty-one of its members are small states, many of them island nations.
The city of Valletta has been put under unprecedented security as it is taking place amid series of terror attacks around the world.
Members of British Royal family -- Prince of Wales and the Duchess of Cornwall are also in Malta. The summit also discussed range of issues relating to climate change so that political support can be drummed up before the Paris Summit.
Malta, a southern European island country comprising an archipelago in the Mediterranean Sea, is hosting the CHOGM for the second time.