The south-coast club faced proceedings at London's High Court over a multimillion-pound unpaid tax bill after talks with the British government's Revenue and Customs department (HMRC) failed to produce an agreement.
It now has one week to draw up a statement of its financial affairs and will be back in court on a date after February 19.
Portsmouth, FA Cup winners in 2008, are five points adrift at the bottom of the league and had the club been forced to go into administration the team would have faced a nine-point deduction and almost certain relegation.
They are banned from buying players because of money owed to other clubs, while the players and staff have regularly had their salary payments delayed this season.
Last Thursday, Hong Kong businessman Balram Chainrai became the fourth person to own the club this season after becoming frustrated at not receiving payments on a 17 million pounds loan he made to his predecessor.
However, Chainrai said he had no interest in running the club and would offload it as soon as he could find a buyer.
UNPAID DEBTS
In Wednesday's hearing it emerged Portsmouth face a VAT bill of 7.4 million pounds, which the club is disputing, and a 4.7 million pounds charge for unpaid PAYE (Pay As You Earn) and National Insurance contributions which were not part of Wednesday's petition.
Representing HMRC, Gregory Mitchell QC said: "It is quite clear beyond any doubt at all that this company is insolvent. They have failed to provide any evidence at all as to their solvency. There are many debts and they are unpaid."
Court registrar Christine Derrett said "I am very concerned about the financial status of this company. It seems to me there's a very real risk that this company is undoubtedly trading while it is insolvent.
"I am obviously conscious that by making a winding-up order it would have very severe consequences not only for the company as a business but for the supporters themselves but that is not a consideration that I strictly take into account."
Portsmouth chief executive Peter Storrie said later he was confident the club would survive.
"It's still a very serious situation and we've got a lot of work to do but we have a bit more time to prove to the court that we are viable, we can go forward and we've got potential buyers," he told Sky Sports News.
"They are (serious) and also you never know also who might come out of the blue in the next day or two.
"Sometimes it does happen overnight with a surprise name, someone you haven't dealt with before, but certainly the two parties I've been speaking to do seem to have an interest.
"It has been a pretty tough time since the November before last but here we are 15 months down the line, and we are still here and still going," he said.
"There have been some pretty fraught times but... we want to do what is best for the fans and keep the club going. So yes, I'm hopeful we can continue that and still be here completing the season and hopefully staying up."
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