The dialogue call emerged on Saturday from a conservative strategy session led by Dominique de Villepin, the prime minister.
Left-wing parties held their own meeting on Saturday morning before a mass "action day" they have planned for Tuesday.
Jacques Chirac, the president, said on Friday evening that he would sign the legislation, but then effectively declared it dead on arrival by telling de Villepin to follow it up immediately with amendments that would shorten the trial period to one year and oblige employers to justify any firing.
Demonstrators rampaged through Paris and other cities until early Saturday to express their rejection of Chirac's move.
In the capital, protesters smashed shop windows, damaged cars, threw bottles at police and attacked the offices of a member of parliament from the ruling UMP party during a march by more than 2,000 people across the city.
Police said 107 people were arrested and two police officers were slightly injured.
Chirac's long-awaited speech met with flat rejection from his critics and a tepid welcome from a friendly newspaper.
Leaders of the nationwide protests rejected his dialogue call.
"Today is April Fool's Day. If this weren't so serious, I'd think the speech was delivered today," Jean-Claude Mailly, head of the Force Ouvriere union, told Europe 1 radio.
Ruling party leaders called for
talks after meeting on Saturday
The left-wing daily Liberation criticised Chirac for signing the disputed jobs law but asking employers not to use it until a follow-up law modifies its most contested measures.
"This confusion cannot stop the crisis," it said.
Francois Bayrou, head of the centrist Union for French Democracy (UDF) party, said: "This is the first time in history ... that someone signs a law and asks that it not be applied.
"To avoid a crisis, they chose to risk looking ridiculous. I hope they don't end up with both."
The conservative Le Figaro praised Chirac for seeking a compromise but said that all sides - protesters, government and opposition - "must enter the game before events get out of hand for all of us".
The communist L'Humanite said: "His promise of a second law ... is nothing more than a pathetic delusion."
Image at stake
Business leaders fear that more protests could damage France's image and hit investment and tourism, especially since the unrest has erupted so soon after rioting by youths in the poor suburbs around France's main cities late last year.
Bernard Accoyer, floor leader of the governing UMP party, said his faction would introduce a follow-up bill to amend the job law that Chirac plans to sign and then sideline in a manoeuvre widely criticised by protesting groups.
Leaders fear continued protests
could damage France's image
"But first, right at the start of the week, we will do all to open a dialogue with all unions and young people who want to participate," he said.
"Only after these exchanges and this will we submit the new law to parliament."
The disputed law allows employers to fire workers under 26 without reason during their first two years. It is aimed at creating job-market flexibility, but students and unions condemn it as creating a throwaway workforce.
Nicolas Sarkozy, the interior minister and Villepin's main rival to become the UMP candidate for president next year, backed the call for a serious dialogue and urged protesters to join in.
"We are all agreed on this strategy," he said after the meeting.