To avoid risks of new shortages of medical equipment, which dogged the bloc at the beginning of the pandemic in spring, the commission said it had launched joint procurement for gear needed to inoculate people, such as syringes and disinfectants.
It also extended until April a temporary suspension of customs duties and sales tax on the import of medical equipment.
EU countries could also exempt COVID-19 testing kits and vaccines from sales tax, the commission said.
In an additional move aimed at avoiding further disruptions to the EU internal market, Brussels proposed fast-tracking checks on EU internal borders for goods transported by rail, water or air.
Rapid checks were introduced for goods transported by road after internal trade was disrupted at the start of the pandemic due to border controls introduced within the border-free Schengen area to prevent the spread of the virus.
To better trace the spread of infections, Brussels said EU governments should coordinate their testing strategies and make greater use of rapid antigen tests, despite the fact that the global supply for these kits is now tightening.
It said the "current shortfalls in testing capacity" required swift action.
Last week, the EU executive said it would direct 100 million euros ($118 million) to buy up to 22 million antigen tests to meet EU countries' "immediate needs". It is now urging states to buy more through a joint procurement scheme.
It also said states should have common testing requirements for incoming travellers, including tests on arrival if tests were not available in the country of departure. It called for coordinated rules on quarantines.
Brussels also urged governments to share more data on outbreaks in their countries and on the situation in their healthcare settings.
All national applications that allow the operators to trace people exposed to the virus should also be made interoperable across the EU, the commission said.
Von der Leyen said the delivery of potential vaccines to EU countries could begin in earnest in April, and vaccination strategies should give priority to the most vulnerable.
"The big numbers of supplies are due to start in April," von der Leyen told a news conference, adding that in the best-case scenario companies could deliver up to 50 million vaccines a month to the EU.
Earlier this week an EU Commission official told EU diplomats that not enough vaccines would be available until 2022 to vaccinate all the 450 million people in the EU.
The commission said on Wednesday it had already spent in upfront payments about 1 billion euros ($1.2 billion) to secure potential vaccines from AstraZeneca, Sanofi and Johnson & Johnson. That suggested it had made a downpayment worth 360 million euros to Johnson & Johnson, a figure which it had not previously revealed.
It said exploratory talks with Moderna, Pfizer and CureVac involved a further 1.45 billion euros in upfront payments. ($1 = 0.8461 euros)
(Reporting by Francesco Guarascio @fraguarascio, editing by Robin Emmott, Hugh Lawson and Nick Macfie) ((Francesco.Guarascio@thomsonreuters.com; +32 2 287 68 17;))