The motorsport.com website quoted Pirelli motorsport director Paul Hembery as saying there would not be enough time to prepare new, wider tyres planned for 2017 if the governing FIA's Formula One commission stalled on approving rule changes.
Pirelli won a tender for the 2017-19 contract in October but that has yet to be signed off with the International Automobile Federation (FIA) due to the testing issues.
"When I land (in Europe after the Chinese Grand Prix), if I don't have an email confirming it's approved, or something else positive, then you will be calling me for a different story," said Hembery.
"This is it. We cannot do our job without this. We cannot deliver. We are being asked to make very significant changes, by changing the driveability of the tyres."
Hembery and the FIA were not immediately available for comment.
Motorsport.com said Pirelli had written to the FIA earlier in April to make clear that it would withdraw from the 2017-19 contract if the test programme was not sorted immediately.
The website said FIA race director Charlie Whiting had recently visited senior Pirelli representatives in Milan to push the testing agreement forward.
It added, however, that an agreement had been reached in Shanghai, during the weekend's third round of the championship, for five teams to join a programme to run from July for a period of 25 car days.
"There are big changes happening. We are being asked to make big changes, the drivers are asking for change - and yet we are being left without the tools to do it. People can argue we don't need to test, but we do," said Hembery.
Formula One is preparing for major rule changes next season aimed at making cars faster, harder to drive and with more downforce.
As part of the plans, wider tyres will be subjected to heavier loading and faster cornering speeds.
Teams are currently subject to strict limits on track testing before and during the season but the regulations now allow for 12 days of tyre testing. Pirelli also want clarification on what cars and drivers they can use.
Photograph: Julian Finney/Getty Images
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