Malcolm Vincent, 41, a computer technician, was killed at a petrol station in Arzew, 300km (190 miles) west of Algiers, on Tuesday evening when two men tried to steal his car, the official Algerian news agency said. He died on his way to hospital, it added.
Earlier in the day, Max Barbot, a 67-year-old Frenchman, was found shot dead in the village of Larbaa, just south of the capital, where he lived. The two deaths followed the murders last week of a Spanish businessman and a Russian woman. A fifth foreigner, an Italian, was badly wounded in a gun attack.
An ultimatum, delivered in October by the Islamic fundamentalist kidnappers of three French consular workers who were released unharmed after one week gave foreigners until 1 December to leave the country or risk assassination. The ultimatum was signed by the Armed Islamic Group, a fringe fundamentalist movement and violence against foreigners ceased during the month of November.
In the six weeks before that ultimatum was delivered to the French and Algerian authorities, seven foreigners were killed. France responded to the threat by rounding up 88 suspected sympathisers of the banned Algerian Islamic Salvation Front, or FIS.
Yesterday, French police carried out a similar operation against suspected fundamentalists among the Tunisian community. Official sources said the Tunisian authorities had asked France to investigate reports that Tunisian residents were planning subversive operations against their homeland. If previous operations are any guide, most of those detained and questioned were likely to be released after a few hours.
France, believed to be worried that embryonic guerrilla networks in Europe could eventually be used by Iranian extremists who are said to be currently without working terrorist organisations abroad, also moved last month against supporters of the People's Party of Kurdistan, the PKK, who were suspected of organising political violence as well as protection rackets against their own community.
Malcolm Vincent, who lived alone, was working for the British firm Pullman-Kellog, a sub-contractor for the Algerian state oil concern, Sonatrach. The Foreign Office said he was one of 335 British residents registered in Algeria.
Britain, in common with other countries, has advised its nationals to leave Algeria. Apart from foreigners, Algerian intellectuals have also been the target of assassination attempts by Islamic guerrillas in what has become an atmosphere of virtual civil war.
In Paris, Alain Juppe, the Foreign Minister, said France was continuing to try to persuade French citizens to leave Algeria.