"[The situation] does not correspond with the need to declare a state of emergency"
Surayud Chulanont, Thai prime minister
Surayud said he rejected the request by the coup leader because the situation "does not correspond with the need to declare a state of emergency".
Anti-coup protesters led by Thaksin's supporters have been holding small but growing weekly rallies calling for democracy to be restored.
A protest last Friday drew about 1,000 people with some demonstrators throwing rocks, plastic bottles and chairs at the police, and coup leaders fear that another rally this Friday could turn violent.
City officials, after meeting security officials, issued a temporary ban on political rallies at a park between Thursday and Monday but protest organisers immediately switched to a different site in the capital.
Natthawut Saikua, a protest leader, said: "We have been clear from the start that our plan is to use transparent and non-violent means to show that what [coup leaders] have done is illegitimate."
Many Thais are becoming impatient with the interim government for failing, among other things, to prove corruption allegations against Thaksin.
The coup leaders scrapped the previous constitution on grounds that it allowed Thaksin to consolidate extraordinary powers in his hands.
They promised a public referendum on the new charter, followed by elections by the end of the year.