If this tax is applied at a rate of 3 percent, it should bring in an estimated 5bn euros (£4.4bn) in revenues a year for Member States.
European Union antitrust authorities have also been busy investigating the business practices of Amazon, Google and Apple, leading to accusations, which the Commission denies, that it is targeting Silicon Valley.
Tech industry groups have complained that it is wrong to tax revenues as that would unduly hit companies. The second proposal calls for an interim tax which covers digital activities that now escape tax altogether in the EU.
The importance of the tech companies have got into the limelight in the recent days when it was revealed that in association with the political data firm, the 2016 Presidential campaign of Trump was able to access the personal information of the various Facebook users.
On the other side, countries like Luxembourg and Ireland, where taxes are low and many tech companies are based, oppose the idea and argue for a global move within the G20 or the OECD, a rich countries' club.
Multi-national companies insist they break no rules, though Apple - most notably - has faced European Union demands to pay £11bn in back taxes to Ireland following a state aid ruling.
The UK has, for example, announced a number of back-dated agreements to secure more tax from individual firms as it battles for new rules on a global level.
The EU described its solutions as an "interim" tax measure, and is designed as a short-term measure before the EU finds a more comprehensive way to tax profits based on where tech firms do business.
The tax proposal, which would require the approval of all 28 of the EU member states (27 after Britain leaves the EU next year), has the broad support of the biggest EU countries, including Britain, Germany, France and Italy.
EU leaders meeting in Brussels for the European Council summit on Thursday postponed issuing a formal statement on trade until Friday because they were still waiting for Trump's official statement on the exemption.
The plans were also announced at a time when digital firms are under huge pressure over data protection - given the row now engulfing Facebook over alleged misuse. But US Treasury Secretary, Steven Mnuchin, thinks that having gross taxes on internet companies is not fair.
The EU's Mr Moscovici sought to reassure that "these proposals are neither a response to a French request nor a response against the United States".
Trump is planning to impose tariffs of 25 percent on imported steel and 10 percent on aluminum.
Trump's exemption landed just before a Friday deadline, and came after eleventh hour talks in Washington between Malmstroem and top USA officials.