Mahinda Rajapakse told Indian television station NDTV on Tuesday: "They are all Sri Lankans, so we can discuss this ... This is what I am asking them, to come and discuss what they want."
More than 700 people have been killed in fighting this year as attacks blamed on the Tigers are rising.
The situation is exacerbated by attacks on the Liberation Tigers of Tamil Eelam (LTTE) by former rebels known as the Karuna group, and many fear a new civil war can start.
The military accused the Tigers of firing on fishermen and on army positions on Tuesday morning, wounding one member of an anti-Tiger political party. The military had fired back in several incidents.
Rajapakse had previously ruled out yielding to the Tigers' demand for an independent nation in the north and east of the country, but told NDTV that he and a committee of experts were preparing a draft solution for discussion.
"I don't want to give them something and tell them to eat it, we will give them an outline, we can get the LTTE to sit and draft what they want... they can discuss."
Rajapakse's majority Sinhalese Buddhist and Marxist allies oppose concessions to the Tigers; but Norwegian mediators, working closely with India, say they hope the island's peace process can be restarted.
"No faction of the LTTE or Karuna or anyone can come in (government) controlled areas with weapons"
Mahinda Rajapakse, president of Sri Lanka
The Tigers say they will not return to talks until the army stops killing Tamil civilians, but many fear the rebels simply want war.
Diplomats are sceptical of repeated denials that the government gives its backing to fighters led by the former Tiger eastern commander Karuna Amman, who is attacking the LTTE.
"We have said in our territory... we are not allowing anyone to operate," said Rajapakse. "No faction of the LTTE or Karuna or anyone can come in (government) controlled areas with weapons."
But monitors and aid workers in the east say that is not the case. Not only are the Tigers apparently able to enter government areas to attack the military, but they say Karuna increasingly operates with impunity.
The Karuna group denies it has government support, but its camps are widely said to be close to military bases while the army is accused of doing nothing to halt abductions of dozens of young men and children to fight for Karuna.