Sunni militants have advanced through western Iraq after seizing a strategic Syrian border crossing, and with US Secretary of State John Kerry calling for the country’s leaders to rise above sectarianism.

The latest assaults saw the security forces making “tactical” withdrawals on Sunday in the face of an insurgent onslaught that has displaced hundreds of thousands and alarmed the world amid fears Iraq could tear itself apart.

The militants, led by the jihadist Islamic State of Iraq and the Levant (ISIL), seized the towns of Rawa and Ana after taking the Al-Qaim border crossing on Saturday, residents said.

The government said its forces had made a “tactical” withdrawal from the towns, control of which allows the militants to open a strategic route to neighbouring Syria where they also control swathes of countryside along the Euphrates river valley.

ISIL, also known as ISIS, aims to create an Islamic state incorporating both Iraq and Syria, where the group has become a major force in the rebellion against President Bashar al-Assad.

Washington wants Arab states to bring pressure on Iraq’s leaders to speed up government formation, which has made little headway since April elections.

While American leaders have stopped short of calling for Prime Minister Nuri al-Maliki to step down – arguing it is up to Iraqis to choose their own leaders – they have left little doubt they feel the Shi’ite premier has squandered the opportunity to rebuild his country since US troops withdrew in 2011.

“We gave Iraq the chance to have an inclusive democracy. To work across sectarian lines, to provide a better future for their children,” President Barack Obama told CNN on Friday.

“Unfortunately what we’ve seen is a breakdown of trust.”

The seizure of Al-Qaim leaves just one of three official border crossings with Syria in federal government hands. The third is controlled by Kurdish forces.

Anti-government fighters already hold areas of the western desert province of Anbar which abuts the Syrian border, after taking all of one city and parts of another earlier in the year.

Elsewhere, government forces launched an air strike on the militant-held city of Tikrit, killing at least seven people, residents said, as the defence ministry announced air strikes on the northern city of Mosul.

The insurgents also clashed with security forces and pro-government tribal fighters in Al-Alam east of Tikrit, with militants killing the women’s affairs adviser to the provincial governor.

The fighting came as Kerry arrived in Cairo on a trip to the Middle East and Europe, with Washington aiming to unite Iraq’s fractious leaders and repel the militants.