The French Tennis Federation said it hoped the delay could enable more fans to attend if COVID-19 restrictions are eased by then.
Last year's French Open was delayed by four months and held in September and October instead of its longstanding May-June slot.
Discussions between the ministry and Roland Garros officials also included how the tournament might be able to accommodate fans who were largely locked out of the delayed 2020 edition. This year's event is due to take place between 23 May and 6 June.
Fernando Verdasco said he underwent "multiple" tests including in Rome and Hamburg, all of which were negative until he tested positive in Paris on Tuesday.
French Open 2020: 'Millions of euros up in smoke' at Roland Garros, fewer fans, plenty of rain...and 'dangerous' balls
Reduced fan limits is just one of a number of headaches facing the French Open organisers, two days out from the start of the season's final Grand Slam event.
French Open 2020: Grand Slam to allow just 1,000 fans a day due to rising coronavirus cases in Paris
The limit of 1,000 fans a day at Roland Garros represents less than 3% of last year's total attendance of almost 520,000.
Rafael Nadal's bid for a 13th Paris title, and a record-equalling 20th Slam, and Novak Djokovic's pursuit of a second triumph in the French capital, to take him to 18 majors, are vying with health concerns in the battle for public attention.
An FFT statement said it had consulted with the ATP, WTA and International Tennis Federation (ITF) to allow the French Open showpiece the benefit of an extra week.
Coronavirus Outbreak: French tennis federation to launch $38 million relief plan to aid clubs, tournaments and players
Some 21 million euros will be dedicated to the French clubs, nine million will go to the 142 tennis, chair tennis, paddle and beach tennis players outside the top 100, as well as officials and tournaments that had to be cancelled amid the COVID-19 crisis, FFT president Bernard Giudicelli told reporters
Coronavirus Outbreak: French tennis players gingerly return to courts with an eye on safety concerns
"The big risk is to get injured," French tennis player Nicolas Mahut said. "We played leisurely for one hour and there are already a few pains."
French Open organisers in talks with sport’s governing bodies to discuss tennis calendar for second part of season
The FFT’s decision to postpone the French Open from 27 May - 7 May amid the COVID-19 crisis was widely criticised because the new dates clashed with the hardcourt season.
Coronavirus Outbreak: French Tennis Federation launches $38 million support plan amid COVID-19 suspension
Professional tennis has been suspended until mid-July and Wimbledon has been cancelled. The 24 May - 7 June French Open has been rescheduled for 20 September - 4 October.
Coronavirus Outbreak: Tough for game to resume this year, says Tennis Australia chief executive Craig Tiley
Tennis could lose the remainder of the 2020 season to the coronavirus pandemic, Tennis Australia (TA) chief executive Craig Tiley has said.
From Vasek Pospisil to Naomi Osaka, tennis players express displeasure over Roland Garros postponement to September due to coronavirus
The French Tennis Federation (FFT) on Tuesday said the claycourt Grand Slam at Roland Garros would now take place from 20 September - 4 October, dates that clash with several other events
Laver Cup organisers say the exhibition event will go ahead in September as planned despite Roland Garros moving to the same dates as the implications of the French Tennis Federation’s shock gambit began to reverberate on Wednesday.
WTA to offer increased rankings protection for mothers returning to tour after giving birth, reports British media
The Women’s Tennis Association (WTA) will offer greater protection to the rankings of mothers returning to the tour after giving birth, British media reported on Thursday.
Former world number one Amelie Mauresmo has turned her back on becoming France’s new Davis Cup captain, opting instead to work with French player Lucas Pouille
US Open 2018: Rafael Nadal backs Roland Garros' new dress policy after Serena Williams' 'catsuit' row
French Tennis Federation president Bernard Giudicelli created an uproar when he said in comments reported in the French media that some outfits, such as Serena Williams' "Black Panther" catsuit, wouldn't be allowed.
French Open Tennis Federation to ban Serena Williams' 'Black Panther' catsuit that she wore in 2018 edition
Serena Williams stunned Paris this year in her body-hugging outfit which she said was inspired by the 'Black Panther' movie and made her feel like a 'warrior princess'.
French Open serves up largest prize money pot in Grand Slam events this season after Brexit eats up Wimbledon purse
The French Open will this month serve up the largest prize money pot in Grand Slam tennis so far this year, taking advantage of Brexit’s hit on Wimbledon’s purse as it shakes off its old reputation as the poorer cousin of the big four tournaments.