The Barcelona president spoke to reporters after a ceremonial handover event, with the vast majority of questions centred on the Argentine forward.
Laporta said Barcelona had made an official offer to Atletico Madrid that is still valid, though only for a limited period.
He suggested Atletico had so far rejected the approach because they have no ready replacement for Alvarez, and admitted he did not understand the Madrid club's conduct after they lodged a complaint with FIFA.
"I want to make clear that we still have great respect for Atletico," said Laporta.
"The tweets came before Julian said he wanted to play for a big club, he didn't say Barca. Some people interpreted that as Barca, others didn't.
"We haven't forced this, it's been the player. This footballer was in Barca's orbit before he signed for City, and even before that. At that time we couldn't take on the deal. We've made an offer, club to club. We understand they're not selling because they don't have alternatives. When they have alternatives, if they want them, and this offer is still valid, we're interested in doing the deal. Now I see there have been a series of actions.
"I don't see the logic behind this. All of Atletico's representatives are very experienced people and I don't know what their strategy is about. They have our offer, if they want to accept it, we'd be delighted."
Laporta insisted Barcelona were prepared to be patient over the transfer.
"This won't be the first time we've done a deal like this, and they've always gone through, agreed and without problems, apart from one that was conflictive," he said.
"This one is more sensitive, perhaps. We're making a significant effort and it's a proposal we're maintaining for as long as we consider it right. Atletico are closing ranks and I hope they reconsider and accept. If they don't, let them say so and we'll see. But taking this to UEFA, FIFA... I don't know why. Maybe there are people who want to stir things up... it doesn't make sense."
Laporta stressed that any deal for Alvarez would only go ahead on Barcelona's terms.
"Barca can take on any operation, but with sporting and financial logic. We'll set the market ourselves. I've spoken with Atletico and made clear what we want. Deco made an offer. We know the player wants to come to Barca, and has done for a long time. We've made this proposal with total respect for the Madrid club. They told me they had no plans to sell because they don't have alternatives. We'll maintain this offer for as long as we consider necessary. We won't be waiting on whatever they might say. If they want to do the deal, we'd be delighted. The offer isn't open-ended."
The stand-off leaves Alvarez's future unresolved, with Barcelona unwilling to walk away from a deal they believe still has time to develop.
Laporta's insistence that the offer will not stay on the table indefinitely suggests Barcelona expect a decision from Atletico before too long.