* Military calls for talks to end crisis
* Four slightly injured by Bangkok blast
* Gunman fires at protesters, no serious injuries (Adds details)
By Apornrath Phoonphongphiphat
BANGKOK, Jan 19 (Reuters) - Thailand's military chief urged both sides in the country's prolonged political crisis to settle their differences, amid signs that opposition protests against the government could be running out of steam.
Anti-government firebrand Suthep Thaugsuban led thousands in a march through the Thai capital on Sunday demanding Prime Minister Yingluck Shinawatra step down.
Demonstrators' numbers appear to have been tailing off but in a sign of the lingering tension, police said four people were slightly injured in a blast at the site of a protest camp in the centre of the capital.
"Now all of us need to help each other in taking care of our own nation," supreme armed forces commander Thanasak Patimapakorn told local reporters after Saturday's Army Day parade.
His comments followed Friday's grenade explosion in Bangkok that wounded 35 anti-government protesters and killed one, a sudden flare-up of violence in more than two months of protests against Yingluck's government. It brings the death toll to nine since November.
"The relationship between the government and the army is normal ... We need to respect law and order. I myself respect the law and I respect all sides and I request that all sides should come together and talk to find a solution," Thanasak said.
Separately, the Bangkok Post daily quoted Thanasak as saying he had no interest in becoming prime minister himself and acting as mediator in the latest episode in an eight-year conflict pitting Bangkok's middle class and royalist establishment against poorer, mainly rural supporters of Yingluck and her brother, the self-exiled former premier Thaksin Shinawatra.
Speculation has been rife that the military might step in to end the impasse, which is beginning to take its toll on Southeast Asia's second-largest economy.
The army has staged or attempted 18 coups in 81 years of on-off democracy, but it has tried to remain neutral this time.
It was unclear who was behind Friday's attack on protesters. Their leader Suthep blamed the government and said the incident would not dent the morale of demonstrators who have been blockading key arteries of Bangkok and occupying ministries.
Police said an unknown gunman had fired at protesters on Saturday night in Lat Phrao in the north of the capital.
"A bullet hit a 54-year-old man and he was sent to hospital immediately. His condition is OK now," a police official in Lat Phrao told Reuters.
Police said there was a blast at Chitlom, near another protest site in the city centre, but no one was hurt.
"Please, my fellow countrymen, please rise up and do our job, which is to stop this wicked government from functioning," Suthep said in a speech late on Saturday, urging protesters across the country to target government buildings to prevent civil servants working.
But there is little sign that the movement is spreading beyond the capital and into the countryside, where Yingluck has her political power base.
She has called an election on Feb. 2, which the main opposition Democrat Party has said it will boycott. Even if it did contest the election, most political analysts say Yingluck's Puea Thai Party would almost certainly win.
Strong rural support has enabled Thaksin or his allies to win every election since 2001.
The protesters accuse Thaksin and his sister of corruption, and want Yingluck to step down to make way for an unelected "people's council" to push through broad political reforms.
The latest demonstrations are the biggest since pro-Thaksin protesters paralysed Bangkok in April and May 2010. That movement ended with a military crackdown and more than 90 people, mostly protesters, were killed.
Pro-government "red shirt" protesters have stayed outside Bangkok this time, limiting the risk of factional clashes. (Writing by Jonathan Thatcher; Editing by Alan Raybould and Clarence Fernandez)