The Catalan side presented new arrival Ferran Torres, who joined from Manchester City in a deal that could be worth €55 million ($86 million).
The Spain international's arrival came despite Barca's well-publicised financial problems, with debts rising above €1.2 billion ($1.9 billion) last year.
Indeed, the club will be unable to register Torres until it offloads some players as it would otherwise risk exceeding its salary cap, which is also the reason it has had to wait to add veteran Dani Alves to the squad.
Despite the financial constraints, club members voted last month to approve the €1.5 billion ($2.4 billion) Espai Barca project that will see an overhaul of Camp Nou and other facilities, while rumours persist that it will sign Alvaro Morata on a loan deal in this transfer window.
There is also speculation Barca will be at the front of the queue to sign Borussia Dortmund star Haaland this year and Laporta did little to discourage such talk.
Asked about Haaland specifically, he said: "If you'll allow me, I won't talk about particular names. It doesn't help at all. It increases their value.
"We're working to reinforce the positions the coaching team have asked us to. Today, we have Ferran, who is from Valencia, and we're proud because Catalans and Valencianos are first cousins.
"Barca are a benchmark in the market and every player considers us a model. We have a squad under reconstruction, and we'll soon see the resurrection of the team.
"Ferran is the proof: that a top-quality player has shown a desire to come to Barca means the resurgence is a reality.
"Everyone should get ready. We're back."
Laporta added: "We're working with the technical secretary to have a competitive team. Xavi supported the Ferran operation and that's been concluded successfully.
"Anything is possible. We're in the market and we're waiting on everything. Barca continue to be a benchmark. Every player considers the possibility of coming to Barca.
"We're progressing well; everything is working quite well. There are some necessary things for this season, so we can win the maximum number of trophies possible and try to respect the will of our coach. The signing of Ferran is really important for the project.
"Other signings we're thinking about for this market, we'll announce to you. We're working very calmly. We're on track to make new signings in the winter market and the technical secretary is working for next season."