(Adds details of fighting in Sirte)
* Government fighters in Sirte regroup after setbacks
* Clinton visits, urges creation of unified military
* NTC moves new homemade weapon to the front
By Rania El Gamal and Tim Gaynor
SIRTE, Libya, Oct 19 (Reuters) - Libyan interim government fighters relaunched their offensive on the besieged town of Sirte on Wednesday after being pushed back by die-hard Muammar Gaddafi loyalists holed up in the deposed leader's home town.
Hundreds of National Transitional Council (NTC) troops have surrounded the Mediterranean coastal town for weeks in a chaotic struggle to snuff out the last pocket of resistance against the revolution that ended Gaddafi's 42-year rule.
Grad rockets, artillery and tank fire rained down on Gaddafi positions in the centre of the town.
Asked about the government force's slow progress in taking Sirte, one NTC fighter at the front said: "All we can think of is catching the rat Gaddafi. We are taking it slowly, step by step. We have been patient for 42 years."
NTC fighters have deployed an arsenal of homemade weapons. On Wednesday a bulldozer arrived at the front fitted with armour and resembling a small ship, with a pointed prow and port holes. On its front was mounted a tank turret and the sides were made from concrete sandwiched between steel plate.
A man wearing a black ship's captain's hat with gold braid sat atop the contraption as it manoeuvred into place, ploughing into a lamp-post in the process.
Government fighters shouted "Allahu Akbar" (God is greatest) as it made its lumbering progress towards make-shift barricades of vehicles and shipping containers put up by Gaddafi loyalists.
The NTC's failure to seize Sirte, nearly two months since capturing Tripoli, has raised questions about its ability to exert its authority over the entire country and has postponed the launch of its promised democracy programme.
On Monday NTC forces captured the other main Gaddafi stronghold, the desert town of Bani Walid, where the ousted leader's loyalists had put up resistance for two months.
NTC forces were poised a few days ago to declare victory in Sirte, but on Tuesday they were forced to retreat in some places under intense fire.
But a day later, NTC fighters had taken back the lost ground and made further gains so that for the first time government forces attacking from the east and west could see each other's positions through Gaddafi-held enclave.
Fighters reported Gaddafi soldiers had been firing at them wearing civilian clothes so had stepped up security and were closely checking the identities of everyone at the front, including reporters.
But faced with a disciplined and determined force, many NTC fighters theorised the defenders may be guarding a high-value target, perhaps even Gaddafi himself.
"Why else would a sniper try to take on a tank?" asked Jafar Al Sharif who commands some eight tanks positioned in the streets of Sirte pounding the low-rise apartment blocks housing Gaddafi remaining loyalists.
The NTC offensive, by mostly amateur fighters, has been hampered by a lack of coordination. Units which converged on Sirte from Benghazi in eastern Libya and Misrata to the west have lost men when they fired at each other by mistake.
Gaddafi, wanted by the International Criminal Court on charges of ordering the killing of civilians, is in hiding, possibly deep in Libya's Sahara desert.
Even so, U.S. Secretary of State Hillary Clinton hailed "Libya's victory" during a visit to Tripoli on Tuesday.
Clinton was the most senior U.S. official to come to Tripoli since Gaddafi's ended in August. Her visit was marked by tight security, reflecting worries that Libya's new rulers have yet to establish full control over the country.
The United States took part in the NATO bombing campaign that helped Libya's rebels take power, although its aircraft largely played a secondary role to those of Britain and France.
"I am proud to stand here on the soil of a free Tripoli and on behalf of the American people I congratulate Libya," Clinton said. "This is Libya's moment, this is Libya's victory, the future belongs to you."
Inspired by protests in neighbouring Tunisia and Egypt that ended in the overthrow of long-standing autocratic leaders, Libyans rose up against Gaddafi in February, but it took six months of civil war to end his one-man rule.
The NTC lent its backing to another regional revolt on Wednesday, officially recognising as Syria's legitimate authority an umbrella opposition council struggling to overthrow President Bashar al-Assad.
While Gaddafi himself is still at large, his wife, two sons and a daughter fled to neighbouring Algeria shortly after Tripoli was captured by the NTC in August.
Algeria's foreign minister said his country let them in for "humanitarian reasons". The NTC at the time called it an "act of aggression", but has since moved to patch up ties with Algeria.
"Algeria has systematically honoured all its obligations as a member of the international community," Foreign Minister Mourad Medelci told a news conference in Algiers alongside British Foreign Secretary William Hague on Wednesday.
Hague, on a tour of the region, said he respected Algeria's position but had requested all countries in the region honour obligations to turn over any indicted war crimes suspects. (Additional reporting by Yasmine Saleh in Tripoli and Adrian Croft in Algiers; Writing by Jon Hemming; Editing by Peter Graff)