BERLIN (Reuters) - German engine maker MTU Aero Engines is cautious on further increases in the production of single-aisle jets, saying the supply chain is already tight.

Asked about comments by Airbus that it would like to increase production to 70 a month over an undefined period, MTU Chief Programme Officer Michael Schreyoegg said: "The supply chain is under so much pressure at the moment, dealing with this incredible ramp-up."

Airbus said on Wednesday it planned to increase production of single-aisle A320-family aircraft to 63 a month next year, although the head of French engine maker Safran struck a cautious note on further increases.

Schreyoegg said adding to pressure on the ramp-up in production of top-selling jets such as the Airbus A320 or the Boeing 737 was the introduction of new engines, such as the geared turbo fan for the A320neo, and a growing market for spare parts.

"We have incredible growth in the aftermarket and in the new deliveries market, that's why we are cautious with our commitments," he said at the Berlin ILA air show.

"We have a very steep ramp-up in front of us and the whole supply chain is stretched," MTU CEO Reiner Winkler said. "I think it's better to stabilise this ramp-up and then take it step by step. It's too early to commit to targets without knowing what the effect is on the supply chain."

MTU has made a good start to the year, Winkler added, although said it was too early in the year to make changes to its annual guidance.

MTU is due to report first-quarter results on May 3.

(Reporting by Victoria Bryan, editing by David Evans)