EU nations have until Friday to opt out of the plan, which will relax national protection of tightly guarded defense industries. Officials said only Poland, Spain and Hungary were considering joining Denmark in not signing up to the plan.
Denmark decided in the early 1990s not to participate in the EU's defense policy.
After meeting with EU defense ministers, Witney said he still hoped Poland, Spain and Hungary would decide to participate in the "code of conduct" on defense purchases, scheduled to come into force on July 1.
Polish Defense Minister Radek Sikorski said his government was in the midst of "intensive consultations" with the defense industry and trade unions regarding the EU procurement code. He said the Cabinet would likely decide on Tuesday whether to join.
EU foreign policy chief Javier Solana praised the Polish government's "constructive thinking" on the issue, the AP reports.
Governments have been able to protect their national defense industry champions because military contracts have been largely excluded from EU legislation that has torn down barriers to trade within Europe in other sectors. The new rules will not apply to companies from outside Europe.
EU officials say more than half the annual spending on new military equipment in Europe currently lies outside EU free market rules. Ministers hope increased competition will drive down prices for new weapons.
By allowing companies to compete more in each others' markets, the EU hopes to encourage a restructuring of the continent's fractured industry so it is better placed to take on international rivals.
The rules will apply to defense contracts over Ђ1 million (US$1.3 million), but exemptions will be allowed if ongoing operations dictate that nations need especially quick supply.
Witney urged minister to increase spending on research and technology which currently only accounts for 1.5 percent of the Ђ180 billion ($232.45 billion) total which the 25 EU nations spend on defense every year.
Diplomats said Solana suggested they should aim to raise that figure to 2 percent by 2010 and French Defense Minister Michele Alliot-Marie warned that failure to develop research spending could see European defense industries slipping behind emerging Asian competitors.