* Fight against Islamist militancy also on Kerry agenda
* Tunisian uprising in 2011 inspired revolts across Arab world
* Tunisia's advances contrast with setbacks in Egypt, Libya (Adds details on cooperation)
By Arshad Mohammed and Patrick Markey
TUNIS, Feb 18 (Reuters) - U.S. Secretary of State John Kerry on Tuesday praised democratic progress in Tunisia, where the "Arab Spring" began, and offered to help the North African country's fight against Islamist militants.
During a brief visit to Tunis, Kerry said Tunisia and the United States would start a strategic dialogue, usually meaning regular high-level meetings, beginning with a trip to Washington by Tunisia's premier.
After a crisis last year brought on by the killing of two opposition leaders, Tunisia adopted a new constitution and the ruling Islamists stepped aside for a caretaker administration to govern until elections.
Kerry's visit was to highlight progress since the 2011 uprising that brought down autocrat Zine el-Abidine Ben Ali as well as the compromises new Tunisian leaders have made, unlike their Egyptian and Libyan counterparts, said U.S. officials.
"I wanted to come here today to confirm on behalf of the American people and President Obama our commitment to stand with Tunisia and the people of Tunisia and to help move down this road to democracy," Kerry said after meeting Tunisian President Moncef Marzouki and Prime Minister Mehdi Jomaa.
Tunisia's new constitution and steps to full democracy have been praised as a model in a region still widely unstable since popular revolts in 2011 that ousted long-standing rulers in Egypt, Yemen and Libya.
Egypt's military last year ousted its democratically elected Islamist president after mass protests against his rule. Libya is floundering in disorder with a weak central government unable to impose its authority on rival political factions and brigades of former rebels.
Kerry addressed the many challenges still facing Tunisia, among them persistent violence by Islamist militants whose leader has pledged allegiance to al Qaeda's North African wing, officials said.
Kerry said he had discussed Tunisian requests for more assistance, following the U.S. provision of $400 million since Ben Ali's downfall, and that included more counter-terrorism aid though he declined to say what exactly the United States might provide.
"Most of the requests were focussed on equipment, although there is some thought about training and assistance in other ways, but that has to be discussed thoroughly," he said.
U.S. officials said they would hand over a mobile command post for conducting terrorism investigations and a mobile crime laboratory on Wednesday.
Tunisian security forces have been battling militants from the banned Islamist movement Ansar al-Sharia, one of the radical groups to emerge after Ben Ali's fall.
Ansar al-Sharia was blamed for inciting the storming of the U.S. embassy in Tunis on Sept. 14, 2012 and has since been listed by Washington as a terrorist organisation, with ties to al Qaeda in the Islamic Maghreb.
Kerry's visit to Tunisia is the first by a U.S. Secretary of State since that incident, which occurred three days after an attack on a U.S. diplomatic mission in Benghazi in Libya killed the U.S. ambassador and three other Americans.
U.S. officials had earler said Kerry would press Tunisia to step up efforts to arrest the attackers. (Editing by Mark Heinrich)