AFTER many debilitating jabs, Yemen's Houthi rebels appear to be moving in for the kill against the staggering government of President Abd Rabbo Mansour Hadi. The mostly Shia militiamen burst out of their northern redoubt in 2011 and advanced progressively into the capital, Sana’a, by cannily exploiting the country’s power vacuum, engaging in populist politics and launching a series of well-timed attacks. They took over much of the city in September. On January 20th, following two days of fighting, they took over the presidential palace.

Mr Hadi was said to be hiding at his private home, surrounded by armed foes. A temporary ruling council to replace Mr Hadi has been mooted, but in a televised speech, Abdelmalek al-Houthi, leader of the Houthis, held back from ordering the president out of office. Instead he issued a series of political demands that would in effect leave the Houthis in the driving seat. If they were not met, he said, his revolution would know "no limits".

The Houthis (who prefer to call themselves Ansar Allah, or the Partisans of God) were operating alongside allies of the former president, Ali Abdullah Saleh, who was toppled in 2011; together they form the so-called “Popular Committees”, militias that control a growing chunk of northern Yemen.

The rolling coup has been a long time gathering. A once-marginalised movement emerging from the Zaydi branch of Shia Islam, whose devotees make up about 40% of Yemen's population, the Houthis fought against the army in the northern province of Saada between 2004 and 2010. With the revolt that overthrew Mr Saleh they have grown into the country’s most potent force. In September, when they seized control of much of Sana’a, they stopped short of ousting Mr Hadi but secured a greater say in the affairs of government.

The latest fighting was precipitated by the completion of a new draft constitution which, the Houthis say, enshrines a six-region model backed by Mr Hadi but which they oppose on the grounds that it weakens the country. On January 17th Houthi gunmen abducted Mr Hadi’s chief of staff, Ahmed Awad bin Mubarak, while he was travelling to a meeting with a national body charged with ratifying the constitution. In his speech, Mr Houthi claimed that the president and his aide planned to force the decision on federal regions through without allowing further debate on the topic.

The situation deteriorated after the abduction, with Mr Hadi ordering the Presidential Guard, the only military unit still loyal to him, to secure key locations in the capital. But Mr Hadi came out worst, and his already feeble grip on power was further weakened.

If a ruling council is formed to replace the president it is likely to work to the benefit of Mr Saleh, who has long sought to destabilise Mr Hadi’s presidency, and is believed to have helped the Houthis take Sana’a. The Popular Committees that have patrolled the streets of the capital are made up in equal measure of Houthi and Saleh supporters. Sources in the capital say that the bulk of the fighting against Mr Hadi’s loyalists is being led by the Republican Guard, an elite military unit led until 2013 by Ahmed Ali Saleh, the son of the ousted president.

Many in Sana’a worry that even if Mr Hadi is ousted, the fighting will not stop. Soon, they fear, the Saleh-Houthi coalition will begin to unravel.

The turmoil in Yemen is borne of long-standing internal rivalries and the country’s endemic instability. But America and especially Saudi Arabia will see in the Houthis a dangerous extension of Iran’s power. Iran already provides military help to the governments of Iraq and Syria against Sunni insurgents, among them the jihadists of Islamic State, and is the power behind Lebanon’s Hizbullah militia. Iranian officials, for their part, seem more than happy to feed Saudi fears.

Saudi Arabia last year froze all funding to Yemen in response to the Houthi takeover of Sana’a, while America led the push for UN sanctions against senior Houthi military commanders. While neither government is likely to intervene militarily, a Houthi-run Yemen is likely to become increasingly isolated and economically unstable. That could, in turn, strengthen both southern Yemeni separatists and al-Qaeda’s dangerous Yemeni branch, which claimed responsibility for the attack in Paris against the offices of Charlie Hebdo, a satirical newspaper that had published cartoons of the Prophet Muhammad. The consequences of instability in Yemen extend far beyond its borders.