Murray replaced Roger Federer as the second best player in the world - behind Novak Djokovic - after winning the Miami Masters last month.
It follows his best year to date in 2012, when he took Olympic gold and silver medals in London as well as lifting his first-ever grand slam trophy at the US Open.
Tennis coach Judy Murray said her son, Britain's number one player, is now looking ahead to his next competition at the Monte Carlo Masters.
"He's been number two before - he was was two in 2009 for a short while," she said.
"It's another step to where he would ultimately like to get to and it means that, for the next wee while at least, in the major events he will find himself in the opposite side of the draw to Djokovic who, of course, is the one everybody wants to avoid if they can.
"It's a great achievement for him to get to number two.
"He stayed on in Miami to train in the heat and on the red clay, and he heads out to Monte Carlo today to start preparing for the Monte Carlo Masters which begins at the weekend."
Ms Murray was speaking during a visit to a newly-refurbished tennis facility in Glasgow, which has been upgraded as part of a £1.3million project across the city designed to encourage more people to get involved in the sport.
She joined in with children playing on the courts in Drumchapel Park and showed them some of her expertise.
Resurfacing works have been carried out on all four of the park's four courts and floodlights installed.
The community tennis pilot project is being led by Glasgow City Council and supported by the Lawn Tennis Association (LTA) and the Tennis Foundation.
The pilot, which is one of eight across Britain, is being used to build community engagement and help identify what works best for the sport at a local level.
Ms Murray said: "When I came here in October/November time, the courts were pretty derelict.
"Although there was some activity going on, they were actually unsafe so really to be able to come back a few months later and see them with an all-weather surface, new fencing, floodlights, a good little pavilion, and right in the heart of the local community, is crucial.
"It all starts at grassroots. This is the sort of project that we need to really help us to grow the game, to grow the numbers, to get more people playing."