The Facebook website has lost 10 million visitors in the US and seen no growth in monthly visitors in the UK over the past year, according to data from market research firm Nielsen.

Research shows that the number of unique visitors to the Facebook website from computers, smartphones and tablets has fallen from 153m in March 2012 to 142m in March this year, having peaked at 158m last August.

The news came as Facebook announced its latest quarterly results, saying it had 1.11 billion monthly active users around the world, up 23% from a year ago. Mobile monthly active users were 751 million, up 54%. But much of the growth is coming from poorer nations, where advertising revenues are lower.

Created nine years ago as a website, Facebook is now competing with rival social networks such as messaging service WhatsApp, which were invented as applications for the smartphone age. While the Facebook app is increasingly replacing its website as its members' favourite way of checking in, the surge in mobile users may not be enough to offset falls in PC visits.

In the UK, visitors peaked at 28 million in October before declining to 26 million in March according to Nielsen data on home and work users. As of March, the Facebook website had no more UK visitors than it did a year ago, suggesting that its expansion has plateaued.

A global market research firm, Nielsen collects its data in two ways: it places "tags" on Facebook's servers, with the company's permission, which count the number of browsers, and it monitors the browser activity of consumers in each country.

In the UK, the firm has a 40,000-strong panel that gives a representative sample of the population according to demographic, income, age and location.

The data counts the number of individual browsers on the Facebook website using any type of device, but does not include the numbers of people using the Facebook app. Nielsen said an app user would have to access the full website only once a month to register in its numbers.

The data underlines trends seen elsewhere. On Sunday, the Guardian reported that Socialbakers, which produces Facebook traffic estimates for advertisers, had recorded falls in monthly visits in the US and Europe. The company's chief executive, Jan Rezab, cautioned against using Socialbakers figures in a blog on Monday, saying they were "rough estimates and cannot be used to determine Facebook traffic". However, Nielsen stands by its numbers, which paint a similar picture. Facebook declined to comment.

But the company has said that in developed markets, the number of users accessing from personal computers is falling, while traffic from mobile devices is surging. By Christmas, more than half its visitors – 680 million a month – were using mobile devices. Nearly a quarter of Facebook advertising revenue is generated by the small screen.

Mobile visitors are more valuable to Facebook. Founder Mark Zuckerberg told investors last year: "Someone who uses only our desktop product has only a 40% likelihood of using Facebook on a given day. But someone who uses mobile has a 70% likelihood of using Facebook on a given day. This stat is surprising to many people and very good news for our opportunity on mobile."

Facebook made $219m in the first three months of the year, compared to $205m in the year-ago period. Revenues in the first quarter totaled $1.46bn, versus $1.06bn in the year-ago period. Mobile ads accounted for 30% of total advertising revenues in the first quarter, up from 23% in the fourth quarter of 2012.

This article was amended on 3 May 2013. The original version referred to Facebook users where visitors to the Facebook website was meant, and referred to Nielsen cross-checking "by surveying consumers in each country", when in fact it monitors browser activity rather than surveying consumers. It also said Nielsen "cannot count the numbers of people using the Facebook app", where what it should have said is that the data referred to does not include the numbers using the app.