DUBAI—Airbus SE said it can’t ramp up production of its popular single-aisle jet fast enough to meet demand and forecasts delivery constraints for another three years as airlines clamor for new planes again.

Airbus Chief Financial Officer Dominik Asam, in an interview ahead of the Dubai air show that started Sunday, said airlines are asking for delivery of new aircraft after most of them stopped ordering new jets and tried in many cases to defer or cancel orders during the Covid-19 pandemic. Airbus is pushing sales—what the...

DUBAI—Airbus SE said it can’t ramp up production of its popular single-aisle jet fast enough to meet demand and forecasts delivery constraints for another three years as airlines clamor for new planes again.

Airbus Chief Financial Officer Dominik Asam, in an interview ahead of the Dubai air show that started Sunday, said airlines are asking for delivery of new aircraft after most of them stopped ordering new jets and tried in many cases to defer or cancel orders during the Covid-19 pandemic. Airbus is pushing sales—what the industry calls sales “campaigns”—but is constrained on what it can promise, Mr. Asam said.

“There is a really vibrant activity on campaigns, especially on the single aisle,” he said. “One real challenge we face is the lack of near-term delivery slots.”

After slashing production amid the pandemic last year, Airbus earlier this year told suppliers to start ramping back up, optimistic that demand would snap back. But aerospace suppliers—just like other manufacturers around the world—have struggled with supply-line disruptions and soaring costs. Mr. Asam said they can’t make parts and components fast enough to allow Airbus to deliver all the jets it thinks it can sell. Each aircraft has about 500,000 parts and components. Airbus receives some 1.7 million parts a day across its factories, he said.

Airbus said earlier this month that it faced delivery shortfalls as it struggles with on-time delivery of components and quality lapses. The restart in production of Boeing Co. ’s 737 MAX after its recertification is also adding pressure to the aerospace supply chain.

Mr. Asam said that is all hurting Airbus’s ability to sell new planes. Boeing is outselling Airbus this year, for the first time since the grounding of the 737 MAX, the rival to the A320. He said Airbus is also balking at customers who are pushing for the “fire-sale pricing” that was available during the peak of the crisis last year. With a lack of delivery capacity, those prices are no longer viable.

“There is more pressure now because there is a scarcity of [delivery] slots,” Mr. Asam said. He said airlines are asking to take planes between 2022 and 2024. “For us, there are severe constraints on that time window,” he said.

In a signal of the demand for new aircraft, Airbus on Sunday reached a deal for 255 new narrow-body aircraft from a consortium of airlines backed by private-equity firm Indigo Partners, including Colorado-based Frontier Group Holdings Inc. and Hungary’s Wizz Air Holdings PLC.

Airbus Chief Commercial Officer Christian Scherer said deliveries of those aircraft—all A321neo variants—will trickle over the next few years with the vast majority scheduled for the second half of the decade.

Airbus has outlined plans to exceed its pre-pandemic production rates of its A320neo single-aisle after cutting rates by more than a third at the start of the pandemic. It plans to lift production to 65 a month by 2023. The plane maker is also aiming to go further, telling suppliers that it wants to lift that rate to as many as 75 a month by 2025 or possibly higher. Airbus Chief Executive Guillaume Faury

said Sunday that the Indigo deal supports that plan.

The higher rate proposal has triggered pushback from some suppliers and from leasing companies, who have warned that with travel still subdued, Airbus risks flooding the market.

“I’m trying to convince our [supply] partners to come along,” Mr. Asam said. “We also will probably need more support from our customers going forward to help us do that.”

Boeing has been more subdued over its output plans after halting all production of its popular single aisle for more than four months in 2020. It aims to reach 31 737 MAX jets a month next year before deciding on increasing that.

After burning through cash at the peak of the pandemic, Airbus has since rebuilt its cash levels thanks to continued deliveries of the A320neo—Airbus’s most profitable program.

That cash is critical to supporting Airbus’s new development programs in the coming years, Mr. Asam said. It is providing funds for a longer-range variant of its A320neo, dubbed the A321XLR. It is also funding the recently launched freighter version of its A350 wide-body. Airbus also wants to develop a hydrogen-powered jet for entry in service in 2035. The latter is expected to cost in the “low double-digit billions” at least, Mr. Asam said.

After two slow months of deliveries, the CFO said he is still confident that Airbus will hit its target to deliver 600 aircraft this year. “We have a lot remaining to do for November and December, but you’ve seen in prior years that we were able to handle such orders of magnitude,” Mr. Asam said. “It will certainly be a run towards the finish like every year, but we are still sticking to that 600 aircraft delivery guidance for 2021.”

Write to Benjamin Katz at ben.katz@wsj.com