"Equities are higher, albeit off their best levels and still close to recent record highs," said Accendo Markets analysts in a note to investors.
Nevertheless, Oanda analyst Craig Erlam felt that markets could soon be entering "wait and see mode ahead of the start of the earnings season."
With the first corporate earnings reports expected from Friday and an absence of notable economic events at the start of the week, a note of caution could start to creep in, Erlam said.
"Equity markets in the US are trading at record highs and with high expectations for earnings season already baked in, there may be an element of caution among investors who will be eagerly anticipating the first batch of results."
Around 1440 GMT, London's benchmark FTSE 100 index was up 0.4 percent compared with the close on Monday.
"Once again the FTSE is flirting with a fresh all-time high, and once again it appears to lack the momentum to truly break through and provide a sequel to its end of 2017 rally," noted Connor Campbell, analyst at traders Spreadex.
In the eurozone, Frankfurt's DAX 30 won 0.2 percent and the Paris CAC 40 rose 0.6 percent -- as data showed unemployment falling to the lowest level for nine years in the single currency area.
The EU's official statistics agency said that the jobless rate in the single currency area fell to 8.7 percent in November from 8.8 percent in October, in line with analyst expectations.
In Britain, data showed that retailers saw a slowdown in sales over the crucial Christmas trading period, with shoppers squeezed by higher prices and stagnating wages.
Retail sales rose 1.4 percent last month from a year earlier, according to a survey from the British Retail Consortium (BRC) and financial group KPMG.
In Asia, Hong Kong's main stocks index rose 0.4 percent, equalling its best run of gains since October 2012 and putting its record high in view.
Shanghai finished 0.1 percent higher -- an eighth-straight gain -- and Tokyo closed up 0.6 percent, at its highest closing level since November 1991, as traders returned from a long weekend break.
But Seoul closed down 0.1 percent after a more than three-percent drop in market heavyweight Samsung Electronics, which was hit after its forecast for record fourth-quarter profits missed expectations.
- Dollar steadies -
The dollar held onto its gains against the pound and euro, consolidating its recent mini-rebound with the single currency unable to make inroads despite data showing eurozone economic sentiment at its highest since 2000.
However, with US President Donald Trump's tax cuts already priced in and the European Central Bank expected to begin winding down its stimulus, analysts say the greenback will likely face further pressure from the euro down the line.
Oil prices ticked higher after a positive start to the year driven by unrest in major producer Iran and a depressed economy for fellow OPEC member Venezuela.