Halo: The most popular game on Xbox
The console's price was dropped last month to match the cost of its rivals after reports of sluggish sales in Europe.
The machine now sells for 299 euros (£199), the same price as the market leader, Sony's PlayStation 2, but about £70 more expensive than Nintendo's GameCube, which launched last week.
Nintendo has said that it sold about 75,000 of its machines in the UK in the first two days of sales, and is confident of selling all of its first shipment of 500,000 consoles across Europe in the coming days.
'Marathon'
Microsoft have also reaffirmed their long-term commitment to Xbox.
"This is a marathon, not a sprint and these initial figures are extremely encouraging," said Sandy Duncan, vice president for Xbox Europe.
However, exact sales figures have not been released.
"Our customers have reacted positively to the price drop and we have seen an uplift in sales [of Xbox] since 26 April," said Alex Croft, head of buying for Game stores.
"I'm glad that more gamers in Europe are able to experience Xbox for themselves," said Mr Duncan.
'Great games'
He added: "The new price allows us to be more competitive and make serious inroads into the hearts of European gamers leading up to Christmas 2002.
"But it is delivering great games and great experiences to hundreds of thousands of happy consumers in Europe over the long term that is our most important goal, and we will continue to drive initiatives to continue this cycle of success."
Many industry observers predict that the long-term success of each of the consoles will be determined by sales during Christmas 2002.