After meeting Macron, Philippe Martinez of the powerful CGT confederation said he had the impression that the September deadline had become less definite.
The suggestion was immediately denied by a statement from the president's office, which added that the changes would be passed by decree, another controversial proposal.
Macron also met the leaders of two other union groupings, the CFDT and Force Ouvrière (FO), before moving on to employers' groups, starting with the very vocal Medef, which has enthusiastically supported changes to labour law.
Laurent Berger of the CFDT, the only major union to support the previous government's labour reforms, commented that the president seemed "determined to carry them out" but "ready to listen", while FO's Jean-Claude Mailly said he felt there was "room for manoeuvre".
But few details seem to have been revealed and the unions are definitely opposed to one key proposal, to put a cap on amounts that industrial tribunals can award for unfair dismissal.
Other possible changes include allowing company-level agreements to overrule industry-wide ones on questions such as working hours and referendums initiated by employers, which would effectively cut out the unions.
During the presidential campaign Macron said his aim was to "liberate labour and the spirit of enterprise", claiming that his proposals would bring down France's 10 percent unemployment rate.
The previous Socialist government's labour reform was forced through parliament after six months of demonstrations and strikes.
Macron wants parliament to pass an enabling act that will allow him to put through his changes by ordonnance, a process that speeds up the process.
The parliamentary leader of the mainstream right Republicans, Christian Jacob, opposed that idea on Tuesday.
"To avoid demonstrations we need an open debate [in parliament]," he said, adding that on some questions "we want to go further".
The parliamentary leader of the small Left Radical party, Roger-Gérard Schwartzenberg, called on the government to publish its proposals before the 7 June general election, so that voters can be "really informed without any ambiguity".
Left up in arms
Communist Party chief Pierre Laurent said that forcing the legislation through would be a "way of not wanting to confront democratic debate", especially doing so during the summer, when workers are on holiday,
Former presidential candidate Jean-Luc Mélenchon's France Insoumise denounced a "government of the Medef", pointing to a number of appointments to minister's offices from private industry, including the chief of staff at the labour ministry, Antoine Foucher, who was previously director of human resources at Schneider Electric.
Government spokesman Christian Castaner warned the unions that "people don't have the right to bring France to a standstill when they don't agree with a measure".
"Today dialogue must be accepted but the unions also have to understand the need to make things happen," he told France 2 TV.
Unions and bosses' representatives are to meet Prime Minister Edouard Philippe and Labour Minister Muriel Pénicaud on Wednesday to discuss the timetable.
Public Finance Minister Gérald Darmanin started discussions with public-sector unions, who are dismayed at the abolition of a ministry devoted to the civil service, on Tuesday.