The European Union’s executive body on Wednesday pledged to pursue new rules for taxing internet giants, such as Alphabet Inc.’s Google and Facebook Inc., embracing a push within the bloc to squeeze more money out of large multinationals operating in Europe.

The move by the European Commission comes amid a French-led drive for the tax that includes Germany, Spain and Italy. European Commission President Jean-Claude Juncker flagged the tax initiative in a broader statement on the priorities of the bloc’s executive body for the next two years.

Finance ministers from the four countries in a recent letter called on the commission to devise a proposal that would establish an “equalization tax” on the revenue generated in Europe by digital companies so that the amounts raised would “aim to reflect some of what these companies should be paying in terms of corporate tax.”

The four officials aim to spell out their tax ideas, and also drum up support, at a gathering of the bloc’s finance ministers in Tallinn, Estonia, on Saturday.

The push marks the EU’s latest attempt to crack down on what officials see as tax avoidance in Europe and to assure citizens that large companies are paying their fair share, as some governments are still trying to stabilize public finances after the financial crisis.

Officials in France in particular have chafed at how little tax they say tech companies pay. Over the years, they have floated various ideas for clawing back more—including taxing internet advertising and even corporate use of bandwidth or personal data, only to pull back because passing a measure at the national level wouldn’t snare big multinationals.

Instead, France has become a vocal backer of efforts by the Organization for Economic Cooperation and Development to reduce so-called profit shifting, and efforts by the EU to establish a common tax base.

Pressure from Paris rose over the summer, after a French court threw out a €1.11 billion ($1.33 billion) tax bill that France’s tax authority had issued Google, arguing that the U.S. company should have declared more profit—and therefore paid more tax—in the country.

In addition to promising an appeal, France’s new finance minister, Bruno Le Maire, vowed to pursue new tax rules for tech companies. He also worked hard to woo other big Western European countries to support his position, eventually signing up Germany, Italy and Spain, according to a person close to the French finance ministry.

Under Mr. Le Maire’s proposal, which is still being fleshed out, technology companies with revenue above a certain level would be liable to pay a tax on turnover from customers in each EU country. The size of the proposed tax hasn’t been settled, but could end up between 2% and 5% of revenue, the person close to the ministry said. The rate would be intended to reflect what tax governments think companies would pay on profit derived from turnover from customers in EU countries.

That could lead to big tax bills. Facebook reported that in 2016 its European revenue was €2.06 billion, including some countries that aren’t part of the bloc. Facebook declined to comment on the proposal.

Another EU-level measure that has been broached is a tax on online advertising, according to an EU official. However, details are lacking and any concrete proposal would take time, especially as officials seek a rule that would apply to a range of business models, from Airbnb Inc. to Apple Inc. AAPL -0.75%

Executives at tech companies say the proposals are misguided because the firms create the bulk of their value in the U.S., making much of their profit from European revenue taxable in the U.S., as well. But Europeans argue that those profits are fair game to tax because the U.S. lets companies defer taxes on profit they keep offshore. Tech companies often do so via subsidiaries based in countries with no corporate income tax.

A tax on turnover would rest atop the existing tax system, and that simplicity makes it appealing. Countries could pass the new tax without touching the bloc’s patchwork of tax treaties or upsetting a delicate balance between national income-tax regimes, said the person close to the French finance ministry. If approved, each EU member state would implement the tax nationally.

The EU has struggled for years to close tax loopholes because all of its member countries, including low-tax jurisdictions like Ireland and higher ones like Germany, typically must agree unanimously on tax matters.

Regulators in Brussels have found a way around that impediment by using their powers to enforce the bloc’s state-aid rules, homing in on sweetheart tax deals governments have issued to large multinationals. The EU last year demanded that Ireland recoup roughly €13 billion of unpaid taxes accumulated over more than a decade by Apple.

The EU’s Mr. Juncker on Wednesday suggested that approval of tax legislation require only a majority vote, rather than unanimous backing, so that such measures as the coming proposal for taxing tech companies can get passed more quickly.