Mr Abdullah, 73, was talking to the Bangkok Post on the sideline of the first joint seminar of the Thailand-Malaysia Think Tank and Scholar Network, held in Bangkok.
Emphasising that southern violence was a domestic problem for Thailand itself to handle, the former Malaysian prime minister said a "sense of deprivation" was the root cause of the problems.
"I'm no longer the prime minister but I think Malaysia has been consistent in helping Thailand try to solve the southern problem, and that we are there to help in whatever way Thailand requests," he said.
He said the insurgency began many years ago, the approach towards the issue should still be more or less the same -- a continuity of policy that addresses the core concerns or sentiments of the local people.
"We need to understand that it's not about ideology, but about the accumulated disturbing sentiments pressing upon them concerning poverty, the lack of proper education for children and employment opportunities, as well as the sense of being deprived of proper attention," said Mr Abdullah, now chairman of the Institute of Islamic Understanding Malaysia.
Asked what other gesture Malaysia could do to address the immediate problem of violence, Mr Abdullah said he was not in a position to tell either the Thai or Malaysian governments what to do.
But he had talked with "those people" in the past and understood how they felt.
When it was pointed out that successive Thai governments have had policies of engagement, but the violence did not seem to abate, Mr Abdullah said Thailand has been walking the right path.
"But the people need to feel and see that things have been changing or being implemented [for their sake]. It takes time and we need to continue doing so, but on the matter of the violence, you need to really think about why it happens and who caused it to be that way," he said.
Mr Abdullah said that when people get angry, it's better to manage, not try curb, their emotions, to understand the cause and the reasons, and address the core issues.
Mr Abdullah said engagement, not containment, was the key to finding a solution to the southern issues.
He supported the "dialogue process". Talks among various the players would create more understanding and bridge the gap of mistrust.
In his opening speech to the seminar, which was jointly organised by the Direk Jayanama Center, Thammasat University's faculty of political science, Thai Foreign Ministry, Thailand Research Fund, and Malaysia's Institute of Strategic and International Studies, Mr Abdullah made the point that southern Thailand and the northern Malaysian Peninsula could be developed as a great metropolis.
"We have to fix the (violence) problem and get this important metropolis moving, in a similar way to Hong Kong-Shenzhen or Japan-Korea or Singapore-Malaysia," he said.
He noted that moderation and tolerance was the norm these days and should transcend problems around the world.
He emphasised to the seminar that the issues hovering over southern Thailand were demands for development, quality of education, and the desire to be recognised and respected, and to participate in socio-economic opportunities.
"We need to build upon the sound foundation of political and socio-economic capital that we have. We need to look at the bigger picture of the Asean Economic Community in 2015 as well," he said.
He referred to his push for certain initiatives that helped generate the development and prosperity of cross border cooperation-- the Indonesia-Malaysia-Thailand Growth Triangle. Discussions began when he was foreign minister in 1991.
In his interview with the Bangkok Post, he summed up his legacy in addressing the southern violence in Thailand -- that he supported the three Es (education, employment and entrepreneurship), talks between the stakeholders, and completion of the Kelantan-Narathiwat bridge in 2007.