Jihadist fighters in Iraq seized three border crossings into Syria and Jordan and four nearby towns over the weekend, giving the Islamic State in Iraq and the Levant (Isis) control over much of the country's western frontier and directly threatening the country's main power supply.

Isis can now add large swaths of the Iraqi border to a 300km stretch of land it already controls along the Euphrates river, from Mosul in the north to Saddam Hussein's home town, Tikrit, which now gives the group a launching pad for potential attacks on strategic sites, including the lifeblood of Iraq's electricity generation, the Haditha dam. The gains also bring the crisis in Iraq to the doorstep of Jordan, a key ally of the United States.

The latest Isis offensive comes as Iraq's polarised political blocs face a week of intense lobbying to form an inclusive government that could unite the fracturing country.

The US secretary of state, John Kerry, is due in Baghdad on Monday to meet Iraqi lawmakers who had been bitterly divided before the jihadist surge, but have recently been reaching out to the US and Iran with increasing desperation.

The latest Isis offensive in western Anbar province has seen the group take four towns in recent days. Iraqi officials said the militants took over the Turaibil crossing with Jordan and the Walid crossing with Syria after government forces there pulled out. Al-Qaim, a restive town on the Syrian border, fell a day earlier.

The capture of the crossings follows the fall on Friday and Saturday of the towns of Rawah, Anah and Rutba. They are all in the Sunni-dominated Anbar province, where the militants have since January controlled the city of Falluja and parts of the provincial capital, Ramadi.

Rutba is on the main highway from Baghdad to the two border crossings and its capture has in effect cut the Iraqi capital's main land route to Jordan. It is an artery for passengers and goods, though it has been infrequently used in recent months because of deteriorating security.

Iraq's armed forces are outgunned and ill-prepared to deal with Isis, which has rapidly gathered momentum as it has surged across eastern Syria and back into Iraq, where the earliest incarnation of the group was born a decade ago.

In Baghdad, the enmity between the political factions before the Isis attack meant no consensus about a new government was likely to emerge for some time. Iraqi leaders now increasingly believe that Barack Obama is making US help conditional on their first finding a political solution that empowers disenfranchised groups, especially the country's Sunnis.

Iran, which had eclipsed the US as Iraq's main power broker in recent years, on Sunday warned Washington against sending fighter jets into the region. The country's supreme leader, Ayatollah Ali Khamenei, said Iraq needed no foreign intervention. Iran is heavily invested in the defence of Baghdad, with a prominent Iranian general, Qassem Suleimani, in the capital to coordinate the city's defences.

Obama warned in an interview on Sunday that Isis could spread conflict to neighbouring states and pose a "medium- and long-term threat" to the US. "We're going to have to be vigilant generally," he said. "Right now the problem with Isis is the fact that they're destabilising the country. That could spill over into some of our allies like Jordan.

"But I think it's important for us to recognise that Isis is just one of a number of organisations that we have to stay focused on," he said, highlighting al-Qaida in Yemen and Boko Haram in west Africa among others.

The president denied US inaction in Syria and Iraq had allowed the crisis to escalate. "What we can't do is think that we're just going to play whack-a-mole and send US troops occupying various countries wherever these organisations pop up. We're going to have to have a more focused, more targeted strategy and we're going to have to partner and train local law enforcement and military to do their jobs as well."

Last week Obama said he would dispatch 300 special forces to help train Iraq's army, but said they would not have a direct combat role.

The increasingly grim news from Iraq fuelled fresh recriminations in Washington on Sunday, with Republicans turning on the White House and each other.

Senator Rand Paul, who has resisted Republican calls for more intervention, said the US should steer clear of Syria and Iraq. "It's now a jihadist wonderland in Iraq precisely because we got overinvolved, not because we had too little involvement," he told CNN. Why should Americans fight in Iraq if the Iraqi army was unwilling to do so, he said?

Paul, who may seek the party's presidential nomination in 2016, did not rule out helping Shia forces, but said the Sunni extremists advancing on Baghdad posed no immediate threat to the US. "I don't believe Isis is in the middle of a fight right now, thinking, 'Hmm, we should send intercontinental missiles to America?'"

Senator Dianne Feinstein, Democrat chairwoman of the senate intelligence committee, defended Obama's "thoughtful" handling of the crisis, but admitted the intelligence community failed to anticipate the Islamic extremists' breakthroughs.

"You either have to have the technical means up in the sky or in other places, or you have to have assets – people who will give you human intelligence," she told CNN. "This is a different culture. It's very difficult to pierce. The piercing intelligence-wise in terms of humans has been very difficult all along."

Iraq's existence as a state was imperilled, Feinstein went on. "Candidly, I don't know what the US contingency plan is for a complete takeover of Syria and Iraq," she said. "I do know what we're on the foot of is a major Sunni-Shiite war."