Saudi forces hit back relentlessly at Yemen's Houthi rebels earlier today with fighter jets and artillery.

The attack followed a border incident on Tuesday when rebels crossed into Saudi territory, killing at least one soldier, and apparently seized an area known as Jabal al-Dukhan. Saudi forces are now said to have recaptured the territory, killing about 40 rebels in the process.

Numerous reports from various sources say the Saudis also attacked the rebels with air and artillery fire inside Yemen. Possibly special forces are involved on the ground too. According to al-Jazeera, six locations were hit in Yemen, including one that received about 100 missiles in the space of an hour.

Although the Houthis have been alleging Saudi military involvement for some time, Yemen continues to deny it. However, today's statement from the government news agency was not a blanket denial; it merely denied Saudi "air raids targeting Yemeni villages".

Saudi involvement would be unpopular with many Yemenis and admitting it would cause a serious loss of face for the government, implying (probably correctly) that its own military is incapable of handling the situation itself.

Now, though, it's looking as if the Saudis intend to become much more heavily and openly involved. One Saudi source talked to AP of "a sustained operation which aims to finish this problem on our border". If the conflict drags on, this in turn could lead to increased Iranian support for the Shia rebels.

In the light of President Salih's recent call to end the conflict within 10 days, it may be that Yemen and Saudi Arabia have agreed on a combined push to quell the rebellion.

The Yemen Observer's report of Yemeni tanks and artillery destroying houses in a rebel-held district of Saada city suggests the government may be close to regaining control there. That would be a significant breakthrough, though the rebels do have a habit of resurfacing in unexpected places.

Posted by Brian Whitaker, 5 November 2009 at 21.00 GMT.