* Activists: Over 40 dead in attack on base, ensuing clashes
* Battle continues on Thursday, Islamic State tweet "spoils"
* Al Qaeda off-shoot controls up to 35 pct of Syria -activists (Adds detail, background)
By Alexander Dziadosz
BEIRUT, Aug 7 (Reuters) - Islamic State militants stormed one of the Syrian government's last outposts in the northern province of Raqqa in an overnight attack and battled troops holed up in the area on Thursday, killing dozens of soldiers, activists said.
A monitoring group said over 40 people were killed in multiple suicide car bombings carried out by Islamic State fighters and in ensuing clashes.
The Islamic State, an al Qaeda offshoot, has made rapid gains in Syria since it seized northern Iraq's largest city, Mosul, on June 10, and declared an Islamic caliphate on adjoining territory it controls in Syria and Iraq.
Raqqa is a major stronghold of the Islamic State, which took control of the provincial capital and expelled rival Syrian rebel groups at the start of the year.
The group's hardened fighters - many of them foreign - have been chipping away at government holdouts in the area since last month.
Islamic State fighters killed at least 50 soldiers when they took over a base outside Raqqa city about two weeks ago. They also killed around 270 soldiers, guards and staff when they overran a gas field in central Syria about a week before that, according to the Britain-based Syrian Observatory for Human Rights.
"Allahu Akbar (God is greatest), we announce to the Islamic nation news of the total liberation of the 93rd Brigade (military base)," said a Twitter feed which regularly publishes news from Islamic State in Raqqa province.
The Observatory said clashes continued into Thursday and that there were still government troops in the base. It said at least 27 pro-government fighters were killed after three Islamic State fighters blew themselves up in car bombs at the gates and around the base and in the battles that followed.
At least 11 Islamic State fighters were killed, added the group, which monitors violence in Syria through a network of sources. It said "dozens" more were wounded.
Syrian warplanes carried out air strikes north of Raqqa city and in the area of Tabqa, the Observatory said. Tabqa's military airbase would be the only major remaining government outpost in the province with the fall of the 93rd Brigade base.
ISLAMIC STATE ADVANCES
Islamic State supporters posted images on social media showing a tank and other heavy military equipment which they said were "spoils" from the attack on the base. The images could not be verified.
The assault came as Islamic State militants extended gains in northern Iraq, seizing towns and strengthening a foothold near the country's Kurdish region.
Lebanese officials also say their fighters have been active in the Lebanese border town of Arsal, where militants had mostly withdrawn on Thursday after days of clashes with Lebanese soldiers.
The group, once al Qaeda's affiliate in Iraq, formally split with al Qaeda this year after tensions rose over its expansion into Syria and has since risen to become one of the most powerful armed forces in Iraq and Syria.
Al Qaeda's official Syrian affiliate, the Nusra Front, has occasionally clashed with the Islamic State since the split, but the two groups have also fought side-by-side in some regions, such as Syria's mountainous Qalamoun area near Lebanon.
The Observatory estimates that the Islamic State controls about 35 percent of Syrian territory - although much of that is desert.
The government has meanwhile consolidated its grip on the country's more densely populated central areas, including a corridor stretching from the capital Damascus to the Mediterranean coast in the west.
More than 170,000 people have been killed in Syria's civil war, which pits overwhelmingly Sunni Muslim rebels against President Bashar al-Assad, a member of the Shi'ite-derived Alawite minority, backed by Shi'ite militias from Iraq and Lebanon. (Reporting by Alexander Dziadosz; Editing by Raissa Kasolowsky)