Bashir, wanted by the International Criminal Court for war crimes, announced the dialogue in January 2014 but spent more than a year making preparations and negotiating conditions with opposition groups.
Most groups boycotted today's conference, calling instead for a meeting abroad to agree on terms for talks, but Bashir said they could still join.
"We have not and will not close the door to them," he said at the conference's opening session.
"We announce our wish -- if the other side shows a credible commitment -- to have a permanent ceasefire," he said.
Last month, Bashir issued a decree declaring a two-month ceasefire and pardoning any rebel leaders who attend the talks.
But the Sudan People's Liberation Movement-North, which has been battling government forces in South Kordofan and Blue Nile states, and the main Darfur rebel groups did not respond.
The SPLM-N has said the military launched air raids on South Kordofan after the ceasefire was announced.
Several small rebel factions from Darfur also attended the opening.
The talks are aimed at finding a solution to the country's ailing economy and the conflicts in Darfur, Blue Nile and South Kordofan.
Sudan has been under a US trade embargo since 1997 over charges of rights abuses and backing militant Islamist groups.
Its economy suffered a further blow when South Sudan became independent in 2011, taking with it three-quarters of the country's oil production.
More than 300,000 people have been killed in Darfur and some 2.5 million displaced, the United Nations says.
The ICC has indicted Bashir for alleged war crimes, crimes against humanity and for genocide related to the conflict in Darfur.
The SPLM-N mounted its campaign in 2011 in South Kordofan and Blue Nile states.
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