President Chirac yesterday ordered increased security on French borders in response to the recent spate of terrorist attacks in Paris.
He said he had instructed the government to "introduce very firm measures for the strict control of all frontiers".
The President was speaking hours after the judicial authorities announced they had arrested four people from the Lyons area in connection with arms and explosives offences. The four, three French citizens and one Algerian, were detained several days ago during police raids on a housing estate close to the high-speed railway line where an unexploded bomb was found last month. They were brought to Paris two days ago for questioning.
The new border security measures follow the failed explosion of a bomb at a Paris street market on Sunday, when four people were injured, and the discovery on Monday of an unexploded bomb near another market. Police are uncertain whether they are dealing with one terrorist group or several.
Mr Chirac said that "the fact that you can cross borders so easily, without any controls, is a very great help to terrorists", adding: "As of today, there will be very strict control of everyone who crosses."
Asked what this meant for France's accession to the Schengen agreement, which lifts border controls between some of the EU countries, Mr Chirac said France had already delayed full implementation of the agreement and would "talk again if our partners do not take measures to reinforce the frontiers of the Schengen zone".
After the first two attacks - at Saint-Michel Metro station on 25 July, when seven people were killed, and near the Arc de Triomphe on 17 August - investigators were said to have concluded that the same group, probably from the Algerian Armed Islamic Group (GIA), was responsible for both explosions.
Last week France issued an extradition order for an Algerian citizen and presumed GIA member, Abdelkrim Deneche, in connection with the Saint- Michel bombing. Mr Deneche is being held under anti-terrorist provisions in Sweden, but the Swedish authorities said yesterday that their investigations had confirmed his alibi for 25 July. They must now decide whether to release, deport or extradite him.
The French authorities say they have not established whether the last three incidents, the bomb on the Lyons railway line and the two bombs planted near Paris markets, are connected to the earlier attacks. They were much bigger than the first two bombs.
Mr Chirac paid tribute to the police and judiciary for their efforts to prevent terrorist attacks. But he said he was worried by some media reporting, and called on the French media to show "restraint", so as to prevent the terrorists from destabilising French society.
Mr Chirac refused to pin responsibility on any single culprit. The "Islamic fundamentalist connection is the most likely," he said, but he stressed that most Algerians in France were as law-abiding as everyone else.