* Attacks threaten peace deal signed in past two weeks

* Army, rebels trade accusations on who started fighting

By Denis Dumo

JUBA, Aug 28 (Reuters) - South Sudanese rebels and the army have accused each other for the second time this week of attacks, this time barely a day after President Salva Kiir signed a peace deal that looks increasingly fragile.

Rebel leader Riek Machar said that South Sudanese government troops had attacked towns held by the insurgents but army spokesman, Col. Philip Aguer, rejected the accusation and said it was the rebels who had attacked the government soldiers.

Late on Thursday, state television said Kiir had decreed that a permanent ceasefire, meant to end a 20-month conflict, would go into effect at midnight on Aug. 29.

Kiir signed the peace deal on Wednesday but said he had "serious reservations" on a number of provisions in the peace proposals, including plans to demilitarise the capital. During the signing ceremony Kiir said the rebels had attacked government troops in the north of the country.

Kiir's long-time rival Machar, who is expected to become the country's First Vice President under the deal, signed the agreement last week in Ethiopia. Kiir and Machar have signed several ceasefire deals before only to violate them within days.

Machar said in a statement late on Thursday that a government convoy of gunboats and ferries had attacked the rebel-held towns of Tayar and Ganylel in Unity State, which has suffered some of the worst of the violence over its oilfields.

He said the government's latest offensive was aimed at capturing ports in Unity and neighbouring Upper Nile State.

"The government offensive against the SPLM/SPLA (rebels) is continuing unabated despite Salva Kiir signing the Agreement on Resolution of the Conflict in South Sudan," Machar said.

"We are wondering whether the government is genuine on signing the agreement. We condemn the regime's continued offensive in the strongest possible terms."

Aguer said it was the rebels who had struck at them.

"On Wednesday it was the rebels attacking the SPLA in Nhialdiu and the SPLA repulsed them. There are casualties but we don't have the details up to now," he said, referring to another Unity State town.

"Definitely, the army command will implement the government policy and we will only fight in self-defence if the rebels attack our positions."

Kiir, who has led South Sudan since it seceded from Sudan in 2011, last week asked for more time for consultations but was given a two-week deadline to sign or risk U.N. sanctions.

Fighting has killed thousands of people and displaced more than 2.2 million, 500,000 of whom have fled the country since the civil war began in 2013. Many rely on aid to survive. (Additional reporting by Aaron Maasho in Addis Ababa; Writing by George Obulutsa; Editing by Louise Ireland)