Sunni militants in Iraq have seized two more border crossings, one with Syria and one with Jordan, in addition to the four nearby towns captured by insurgent forces since Friday.
Jordan began to beef up border security after the crossings fell Sunday.
Security officials say the Islamic State of Iraq and the Levant (ISIL) is now in control of Qaim, Rawa, Ana and Rutba in Iraq's western Anbar province.
The blitz takes the al-Qaida-inspired group closer to its goal of carving out a purist Islamic state straddling both Syria and Iraq.
Meanwhile, at least six people were killed Sunday by a suicide bomber and a car bomb in the provincial capital of Ramadi. The attack targeted mourners at the funeral of an Iraqi police officer.
In a televised interview, U.S. President Barack Obama warned that the insurgents' strength could grow and destabilize other countries in the Middle East.
The American leader said the U.S. must remain "vigilant," but would not "play 'Whac-A-Mole' and send U.S. troops occupying various countries wherever these organizations pop up."
The United States has begun a new diplomatic bid to unite Iraq's fractious leaders and repel insurgents.
U.S. Secretary of State John Kerry landed in Egypt Sunday at the start of a visit to the Middle East and Europe, mainly to consult with partners about Iraq, where Sunni militants have made new advances in an offensive that has alarmed the world.
Kerry's unannounced stop in Cairo early Sunday was part of a diplomatic mission to push Egypt toward democracy.
While in Cairo, Kerry said the U.S. wanted the Iraqi people to find a leadership that is prepared to represent all Iraqis but that Washington would not pick or choose the leadership in Baghdad.
Kerry also urged Iraqi leaders to rise above "sectarian considerations," and said that Washington was "not responsible" for the crisis.
Kerry will stop in Jordan Sunday before heading to Brussels for the NATO foreign ministers' meeting, and then to Paris for meetings with regional partners and Gulf allies.
Iran's top leader, Ayatollah Ali Khamenei, said Sunday he is against U.S. intervention in neighboring Iraq, where Islamic extremists and Sunni militants opposed to Tehran have seized a number of towns and cities, the official IRNA news agency reported.
The statement by Khamenei was the clearest statement of opposition to a U.S. plan to dispatch of up to 300 military advisers in response to pleas from the Iraqi government and runs counter to speculation that old enemies Washington and Tehran might cooperate to defend their mutual ally in Baghdad.
“We strongly oppose the intervention of the U.S. and others in the domestic affairs of Iraq,” Khamenei was quoted as saying, in his first reaction to the crisis.
“The main dispute in Iraq is between those who want Iraq to join the U.S. camp and those who seek an independent Iraq,” said Khamenei, who has the final say over government policies. “The U.S. aims to bring its own blind followers to power since the U.S. is not happy about the current government in Iraq.”
Khamenei said Iraq's government and its people, with help of top clerics, would be able to end the “sedition” there, saying extremists are hostile to both Shi'ites and Sunnis who seek an independent Iraq.
Earlier on Sunday Iran's President Hassan Rouhani said some countries “feed terrorists by their petrodollars,” in a veiled reference to the Arab Gulf states, and warned that such support would come back to haunt them.
Rouhani has said his countrymen will not hesitate to defend Shi'ite shrines in Iraq if need be, but he has also said, like Khamenei, that Iraqis are capable of doing that job themselves.
Thousands of Shi'ite Iraqis have responded to calls to take up arms and defend the country against the insurgency.
Tehran and Washington have been shocked by the lightning quick offensive, spearheaded by ISIL, that has seen large swathes of northern and western Iraq fall to the hardline extremist group and other Sunni fighters since June 10, including the north's biggest city Mosul.
The towns of Qaim, Rawah, Anah and Rutba are the first seized in the mainly Sunni Anbar province since fighters from the ISIL and their allies overran the city of Fallujah and parts of the provincial capital of Ramadi earlier this year.
The capture of Rawah on the Euphrates River and the nearby town of Anah appeared to be part of a march toward a key dam in the city of Haditha, the destruction of which would damage the country's electrical grid and cause major flooding.
Taking Rutba gives the insurgents control over the final stretch of a major highway to neighboring Jordan, a key artery for passengers and goods that has been infrequently used for months because of deteriorating security.
Iraqi military officials said more than 2,000 troops were quickly dispatched to the site of the dam to protect it. They spoke on condition of anonymity because they were not authorized to speak to the media, Reuters reported.
There was a lull in fighting at Iraq's largest refinery, Beiji, near Tikrit, on Sunday morning.
The site had been transformed into a battlefield since Wednesday as Sunni fighters launched an assault on the plant. Militants entered the large compound but were held off by Iraqi military units.
A black column of smoke rose from the site. Refinery officials said it was caused by a controlled burning of waste.
Chief military spokesman, Lt. Gen. Qassim al-Moussawi, acknowledged the fall of the Anbar towns, saying government forces had made a tactical retreat and planned to retake them. He provided no further details.
The Islamic State and allied militants have carved out a large fiefdom along the Iraqi-Syrian border. Control over crossings like that one in Qaim allows them to more easily move weapons and heavy equipment. Rebels control the Syrian side of the crossing.
Prime Minister Nouri al-Maliki's Shi'ite-dominated government has struggled to push back against the Sunni militants, who have seized large swaths of the country's north since taking control of Mosul on June 10 as troops melted away.
Iraq has requested U.S. airstrikes to help halt the advance, but Obama has yet to order any, and has instead called on Iraqi leaders to form a more representative government in thinly veiled criticism of al-Maliki.
The U.S., however, has been drawn back into the conflict.
It is deploying up to 300 military advisers to join about 275 troops in and around Iraq to provide security and support for the U.S. Embassy and other American interests.
The fighting has threatened to tear the country apart for good, reducing Iraq to separate Sunni, Shi'ite and ethnic Kurdish regions. It has highlighted divisions among regional powers, especially Iran, which has said it would not hesitate to protect Shi'ite shrines in Iraq if asked, and Sunni Saudi Arabia, which has warned Iran to stay out of Iraq.
Iraq's Kurds have meanwhile expanded their territory in the northeast, including the long-prized oil city of Kirkuk.
Relations between the diverse Sunni groups have not been entirely smooth.
On Sunday morning, clashes raged for a third day between ISIL and Sunni tribes backed by the Naqshbandi Army, a group led by former army officers and Baathists, around Hawija, local security sources and tribal leaders said, Reuters reported.
On Saturday, heavily armed Shi'ite fighters paraded in Baghdad in a dramatic show of force aimed at Sunni militants who seized an Iraqi town that borders Syria, widening a western front in an offensive threatening to rip apart the country.
Thousands of fighters loyal to powerful Shi'ite cleric Moqtada al-Sadr have vowed to fight ISIL, which now controls a large portion of northern and western Iraq, and has been moving closer to the capital.
Some information for this report provided by Reuters and AP.