The Pulo website added: "We invite you all to stop making myth after myth and face reality instead."
Pulo, whose leaders are exiled in Sweden, is one of several groups seeking independence for Thailand's provinces bordering Malaysia.
But spearheading the movement are far more radical, powerful and secretive groups.
Another exiled leader who spoke on condition of anonymity, said: "To hurt innocent people in Bangkok, it is not the aim of the separatists.
"We have nothing to do with the bombings."
Meanwhile, Thai leaders said on Friday that security videos at bomb sites indicated that suspects planting the bombs were soldiers and policemen.
Boonrawd Somtas, the defence minister, said investigators had concluded that "the bombers were men in uniform, both green and khaki", referring to the uniforms worn by the military and police.
Leaders also dismissed rumours that have spread throughout Bangkok saying that Thaksin supporters could try to retake power.
Surayud Chulanont, the interim prime minister, said on Friday: "Security forces and intelligence sources have confirmed that the coup rumours were spread by the groups of people linked to the New Year's bombs.
They aim to create a state confusion and chaos."
Surayad said on Thursday that the authorities should be prepared for future attacks, but did not indicate any specific threat.
The string of eight small bombs on Sunday and early Monday killed three people and wounded nearly 40 as the Thai capital celebrated the New Year.
General Sondhi Boonyaratkalin, the army commander who led the coup against Thaksin and now heads the military's Council for National Security, said it was "impossible" that there would be another coup.
There was speculation that the military might be dissatisfied with the performance of the interim civilian government it installed after the coup, and may prefer to take complete power for itself.
There has been a marked increase in the number of troops on the streets of Bangkok and at airports and bus and train stations since the Sunday night bombings.
The interim government, which is supposed to relinquish power after an election expected later this year, has drawn criticism for failing to restore peace in the south and to properly manage the rising value of the Thai baht, which has hurt exports.