The decision is aimed at encouraging competition in a program that critics say has been poorly managed and unfairly favors the Boeing Co.
Northrop Grumman Corp., which had been partnered with the European Aeronautic Defence and Space Co., announced in March that it would not bid because it didn't think it could win. EADS has said it may be interested in competing on its own but needs more time to prepare a proposal.
Morrell said that if EADS provides the Pentagon with official notification of its intent to compete, companies would be given until July 9 to submit their proposals.
"Nobody should confuse our willingness to change the bid deadline to willingness to change any of the plane's military requirements or the way bids will be evaluated," Morrell told reporters.
The program has been the subject of heated political debate among lawmakers, who want to see the contract produce jobs in their home states. European officials, meanwhile, say EADS has been unfairly shut out.
Following a White House visit this week, French President Nicolas Sarkozy said he trusts President Barack Obama's assurance that any new bidding would be "free, fair and transparent" and said that under those conditions, EADS would bid on the contract.
For his part, Obama reiterated that while "the process will be free and fair," the final decision would be made by Defense Secretary Robert Gates.