Google has been given a last chance, and a deadline of "a matter of weeks" by Europe's antitrust chief, to explain how it will end concerns it is abusing its dominant position in search to push its other products, and effectively locking out rival advertisers.

In a significant move, Joaquín Almunia, the European Commission commissioner, has written to Google executive chairman Eric Schmidt warning there are four areas "where Google business practices may be considered as abuses of dominance".

He now wants Google to propose fixes – or else, he warned, the EC will move to a formal investigation which would lead to fines and legally enforceable remedies. Those could amount to billions of pounds, with the EC able to levy up to 10% of the search giant's revenues.

Rivals to Google applauded Almunia's move, saying that whatever it does, its growing control of a number of search-related areas will be reined in. "There are only two outcomes," said one rival, who preferred to remain anonymous. "Either Google takes the easy option, and makes substantial changes, or the EC moves in on it. We now have an endpoint, which is remedies that are binding, and which restore the level playing field."

Google said in response on Monday that it disagreed with the commission's conclusions but that it was happy to discuss the issues further. It controls 86% of the European search market, according to online data tracking service comScore, though other measures put it higher.

Almunia said his letter to Schmidt cited Google's use of its own products in "vertical search" (such as shopping), and its copying of content from competitors such as travel or restaurant guides, which are then provided in search results, as two of his key concerns.

The first, he said, could be preferential treatment that would hurt those rivals; the other could discourage investment that would otherwise benefit internet users.

The two other concerns relate to how Google shuts out rival advertisers when people choose to use its search-related adverts on their own websites, and the lack of portability of advertising campaigns built around Google's Adwords to other search advertising platforms. Google's UK business, which is almost entirely advertising-based, amounted to more than $1.15bn (£727m) in the past quarter, making such portability a key question.

Sources close to Google indicated that Almunia's announcement was the first time he had outlined to it which areas of its business he was concerned about – even though the EC has been carrying out its investigation since November 2010, beginning with a series of letters seeking evidence from a number of Google partners and rivals.

The investigation was sparked by complaints from a tiny British shopping comparison site, Foundem, as well as Microsoft-owned Ciao, the French legal search engine justice.fr, and the German maps company Hotmaps, that their services appeared artificially low on Google's general search results.

Icomp, an internet lobbying group sponsored by Microsoft which has complained about Google's dominance, and whose members include the Premier League, the music licensing organisation PPL, Hotmaps and Foundem, said it welcomed Almunia's statements.

An Icomp lawyer, David Wood, said Almunia "implies that the commission has found that Google's behaviour constituted an abuse of its dominant position in the online search market".

He added that it was vital that any settlement should include measures "to quickly redress the harm caused to European businesses and consumers and are sufficiently robust to ensure that such harm is not repeated".

Almunia said the problems needed to be dealt with quickly because the high-tech industry changes so rapidly. An investigation could drag on for years, by which time such concerns might be obsolete. The EC was criticised in the past for drawn-out battles into Microsoft and Intel, where restorative measures were seen as outdated once introduced.

"Restoring competition swiftly to the benefit of users at an early stage is always preferable to lengthy proceedings," Almunia said.

Google also faces a similar antitrust investigation by the Federal Trade Commission in the US.

Solving the current investigation will not end Google's wrangles with the EC. It has just received the green light from the Chinese authorities to complete its $12.5bn acquisition of Motorola Mobility (MMI), the US handset maker. But MMI is being investigated by Almunia's group over its use of patents that should be freely licensed in lawsuits against Apple – creating a fresh antitrust headache for the company.