* Iraq media adviser denies post has fallen
* Shi'ite fighters parade weapons in Baghdad's Sadr city
* Army spokesman say militants attack Baiji refinery
* Sunni militants fight each other in Hawija
The militants, led by the Islamic State in Iraq and the Levant (ISIL), first moved into the nearby town of al-Qaim on Friday, pushing out security forces, the sources said on Saturday.
Once border guards heard that al-Qaim had fallen, they left their posts and militants moved in, the sources said.
Sameer al-Shwiali, media adviser to the commander of Iraq's anti-terrorist squad, told Reuters the Iraqi army was still in control of al-Qaim.
Al-Qaim and its neighbouring Syrian counterpart Albukamal are on a strategic supply route. A three-year-old civil war in Syria has left most of eastern Syria in the hands of Sunni militants, now including the Albukamal-Qaim crossing.
The Albukamal gate is run by al Qaeda's official Syria branch, the Nusra Front, which has clashed with ISIL but has sometimes agreed to localised truces when it suits both sides.
The head of the Syrian Observatory for Human Rights monitoring group, Rami Abdulrahman, said ISIL had pushed the Nusra Front out from many areas of eastern Syria in the past few days and their capture of al-Qaim will allow them to quickly move to the Syrian side.
ISIL already controls territory around the Albukamal gate, effectively pinching the Nusra Front between its forces in Syria and those in neighbouring Iraq, said Abdulrahman, who tracks the violence.
The al Qaeda offshoot has captured swathes of territory in northwest and central Iraq, including the second city, Mosul. They have seized large amounts of weaponry from the fleeing Iraqi army and looted banks.
World powers are deadlocked over the crises in Iraq and Syria. Shi'ite Iran has said it will not hesitate to protect Shi'ite shrines if asked by Baghdad but Sunni-run Saudi Arabia has warned Tehran to stay out of Iraq.
U.S. President Barack Obama has offered up to 300 U.S. special forces advisers to help the Iraqi government recapture territory seized by ISIL and other Sunni armed groups across northern and western Iraq.
But he has held off granting a request for air strikes to protect the government and renewed a call for Iraq's long-serving Shi'ite prime minister, Nuri al-Maliki, to do more to overcome sectarian divisions that have fuelled resentment among the Sunni minority.
The fighting has divided Iraq along sectarian lines. The Kurds have expanded their zone in the northeast to include the oil city of Kirkuk, which they regard as part of Kurdistan, while Sunnis have taken ground in the west.
The government has mobilised Shi'ite militia to send volunteers to the front lines.
In Baghdad's Shi'ite slum of Sadr City, thousands of fighters wearing military fatigues marched through the streets.
They carried rocket-propelled grenades, semi-automatic rifles and trucks had mounted long-range rockets, including the new 3-metre "Muqtada 1" missile, named after Shi'ite cleric Muqtada Sadr, who has tens of thousands of followers.
Sadr has yet to throw his fighters into the recent wave of fighting but has accused Maliki of mishandling the crisis.
"These brigades are sending a message of peace. They are the brigades of peace. They are ready to sacrifice their souls and blood for the sake of defending Iraq and its generous people," a man on a podium said as the troops marched by.
The fighting, with strong sectarian overtones, is pushing the country towards civil war.
Iraq's largest refinery, Baiji, 200 km (130 miles) north of the capital near Tikrit, has been transformed into a battlefield.
"Last night, three attacks on Baiji refinery were repelled and attackers ... More than 70 terrorists were killed and more than 15 vehicles were destroyed," said Major-General Qassim al-Moussawi, spokesman for the Iraqi military's commander-in-chief.
He showed aerial footage of cars and people being blown up but details of the fighting could not be independently confirmed.
The conflict has displaced tens of thousands. On Saturday evening, 15 people were wounded by a army helicopter strike in the village of Al Bu Saif, south of Mosul city, medics said.
A health official in Mosul said the wounded included two children and seven women. "Most of them are from the same family. Three are in critical condition from shrapnel wounds," he said.
As in Syria, ISIL has started to clash with other Sunni militias in Iraq. In the town of Hawija, ISIL and members of the Naqshbandi Army, made up of former army officers as well as loyalists of Saddam Hussein's former ruling Baath party, started fighting on Friday evening, witnesses said.
They said the clashes, in a dispute over power, killed 15 people.
"Hawija is falling apart," a senior tribal figure from the community said before the clashes. "There are so many groups working with ISIL. Each group has its agenda."
Hawija could be seen as the spark for Iraq's current armed Sunni insurgency. In April 2013, Sunni protesters said security forces shot dead at least 50 of them. They were demanding greater rights from the Shi'ite-led government. After the killings, violence soared in Iraq.